***************************************************************************** * www.FindStat.org - The Combinatorial Statistic Finder * * * * Copyright (C) 2019 The FindStatCrew * * * * This information is distributed in the hope that it will be useful, * * but WITHOUT ANY WARRANTY; without even the implied warranty of * * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. * ***************************************************************************** ----------------------------------------------------------------------------- Statistic identifier: St001532 ----------------------------------------------------------------------------- Collection: Posets ----------------------------------------------------------------------------- Description: The leading coefficient of the Poincare polynomial of the poset cone. For a poset $P$ on $\{1,\dots,n\}$, let $\mathcal K_P = \{\vec x\in\mathbb R^n| x_i < x_j \text{ for } i < _P j\}$. Furthermore let $\mathcal L(\mathcal A)$ be the intersection lattice of the braid arrangement $A_{n-1}$ and let $\mathcal L^{int} = \{ X \in \mathcal L(\mathcal A) | X \cap \mathcal K_P \neq \emptyset \}$. Then the Poincare polynomial of the poset cone is $Poin(t) = \sum_{X\in\mathcal L^{int}} |\mu(0, X)| t^{codim X}$. This statistic records its leading coefficient. ----------------------------------------------------------------------------- References: [1] Dorpalen-Barry, G., Kim, J. S., Reiner, V. Whitney Numbers for Poset Cones [[arXiv:1906.00036]] ----------------------------------------------------------------------------- Code: # code by Jang Soo Kim def delete_elements(P,A): "Return the poset obtained from P by deleting the elements in A" elms = [x for x in P.list() if x not in A] rels = [R for R in P.relations() if R[0] not in A and R[1] not in A] return Poset([elms,rels], cover_relations=False) def add_bottom(P): "Return the poset obtained from P by adding the minimum element 0." elms = ["zero_hat"] + P.list() rels = [["zero_hat",x] for x in P.list()] + P.relations() return Poset([elms,rels], cover_relations=False) def Poin(P,t,omega=0): """ Input: P: a poset or a list of numbers [a,b,c,...]. If P = [a,b,c,...], then P is set to be the cell poset of the partition [a,b,c,...]. t: a variable omega: a labeling of P which is given by default to the first lin ext of P. Output: The Poincare polynomial of the poset P. The bijection from linear extensions to P-transverse permutations is used. """ if type(P) == list: P = Partition(P).cell_poset().dual() if omega == 0: omega = P.linear_extensions()[0] poly = 0 for L in P.linear_extensions(): poly += t^(len(P)-len(get_P_transverse_permutation(P,omega,L))) return poly def get_P_transverse_permutation(P,omega,L): """ Input: P: a poset omega: a labeling of P L: a linear extension of P Output: The P-transverse permutation corresponding to L with respect to omega. """ Q = add_bottom(P) pi = [] while len(L)>0: N = next_level(Q,P,omega,L) pi = pi + N[-1] [Q, P, omega, L] = N[:-1] return pi def next_level(Q,P,omega,L): """ INPUT: Q,P,omega,L Q: poset containing P omega: labeling L: a linear extension of P OUTPUT: [Q1, P1, omega, L1, pi] Q1 = P P1 = P - minimal blocks omega = omega L1 = L restricted to P1 pi = P-transverse permutation of the minimal blocks in P. """ L1 = L pi = [] C = [] # the list of current level elements in P D = [] # the list of current level elements in P that are not minimal in Q B = [] for x in L: if x not in P.minimal_elements(): # If x is not a minimal element in P this level is done. break C.append(x) if x not in Q.minimal_elements(): D.append(x) if omega.index(x) == min([omega.index(d) for d in D]): if len(B)>0: pi.append(B) B = [x] else: B.append(x) pi.append(B) Q1 = P P1 = delete_elements(P,C) L1 = L[len(C):] return [Q1, P1, omega, L1, pi] statistic = lambda P: Poin(P, QQ["q"].gen()).leading_coefficient() ----------------------------------------------------------------------------- Statistic values: ([],1) => 1 ([],2) => 1 ([(0,1)],2) => 1 ([],3) => 2 ([(1,2)],3) => 2 ([(0,1),(0,2)],3) => 1 ([(0,2),(2,1)],3) => 1 ([(0,2),(1,2)],3) => 1 ([],4) => 6 ([(2,3)],4) => 6 ([(1,2),(1,3)],4) => 3 ([(0,1),(0,2),(0,3)],4) => 2 ([(0,2),(0,3),(3,1)],4) => 2 ([(0,1),(0,2),(1,3),(2,3)],4) => 1 ([(1,2),(2,3)],4) => 3 ([(0,3),(3,1),(3,2)],4) => 1 ([(1,3),(2,3)],4) => 3 ([(0,3),(1,3),(3,2)],4) => 1 ([(0,3),(1,3),(2,3)],4) => 2 ([(0,3),(1,2)],4) => 1 ([(0,3),(1,2),(1,3)],4) => 1 ([(0,2),(0,3),(1,2),(1,3)],4) => 1 ([(0,3),(2,1),(3,2)],4) => 1 ([(0,3),(1,2),(2,3)],4) => 2 ([],5) => 24 ([(3,4)],5) => 24 ([(2,3),(2,4)],5) => 12 ([(1,2),(1,3),(1,4)],5) => 8 ([(0,1),(0,2),(0,3),(0,4)],5) => 6 ([(0,2),(0,3),(0,4),(4,1)],5) => 6 ([(0,1),(0,2),(0,3),(2,4),(3,4)],5) => 3 ([(0,1),(0,2),(0,3),(1,4),(2,4),(3,4)],5) => 2 ([(1,3),(1,4),(4,2)],5) => 8 ([(0,3),(0,4),(4,1),(4,2)],5) => 3 ([(1,2),(1,3),(2,4),(3,4)],5) => 4 ([(0,2),(0,3),(2,4),(3,4),(4,1)],5) => 1 ([(0,3),(0,4),(3,2),(4,1)],5) => 1 ([(0,2),(0,3),(2,4),(3,1),(3,4)],5) => 1 ([(0,1),(0,2),(1,3),(1,4),(2,3),(2,4)],5) => 1 ([(2,3),(3,4)],5) => 12 ([(1,4),(4,2),(4,3)],5) => 4 ([(0,4),(4,1),(4,2),(4,3)],5) => 2 ([(2,4),(3,4)],5) => 12 ([(1,4),(2,4),(4,3)],5) => 4 ([(0,4),(1,4),(4,2),(4,3)],5) => 1 ([(1,4),(2,4),(3,4)],5) => 8 ([(0,4),(1,4),(2,4),(4,3)],5) => 2 ([(0,4),(1,4),(2,4),(3,4)],5) => 6 ([(0,4),(1,4),(2,3)],5) => 2 ([(0,4),(1,3),(2,3),(2,4)],5) => 2 ([(0,4),(1,3),(1,4),(2,3),(2,4)],5) => 2 ([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4)],5) => 2 ([(0,4),(1,4),(2,3),(4,2)],5) => 1 ([(0,4),(1,3),(2,3),(3,4)],5) => 3 ([(0,4),(1,4),(2,3),(2,4)],5) => 2 ([(0,4),(1,4),(2,3),(3,4)],5) => 6 ([(1,4),(2,3)],5) => 4 ([(1,4),(2,3),(2,4)],5) => 4 ([(0,4),(1,2),(1,4),(2,3)],5) => 3 ([(0,3),(1,2),(1,3),(2,4),(3,4)],5) => 1 ([(1,3),(1,4),(2,3),(2,4)],5) => 4 ([(0,3),(0,4),(1,3),(1,4),(4,2)],5) => 2 ([(0,3),(0,4),(1,3),(1,4),(3,2),(4,2)],5) => 1 ([(0,4),(1,2),(1,4),(4,3)],5) => 2 ([(0,4),(1,2),(1,3)],5) => 2 ([(0,4),(1,2),(1,3),(1,4)],5) => 2 ([(0,2),(0,4),(3,1),(4,3)],5) => 3 ([(0,4),(1,2),(1,3),(3,4)],5) => 5 ([(0,2),(0,3),(1,4),(2,4),(3,1)],5) => 2 ([(0,4),(1,2),(1,3),(2,4),(3,4)],5) => 3 ([(0,3),(0,4),(1,2),(1,4)],5) => 2 ([(0,3),(0,4),(1,2),(1,3),(1,4)],5) => 2 ([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4)],5) => 2 ([(0,3),(0,4),(1,2),(1,3),(2,4)],5) => 3 ([(0,3),(1,2),(1,4),(3,4)],5) => 3 ([(0,3),(0,4),(1,2),(2,3),(2,4)],5) => 2 ([(1,4),(3,2),(4,3)],5) => 4 ([(0,3),(3,4),(4,1),(4,2)],5) => 1 ([(1,4),(2,3),(3,4)],5) => 8 ([(0,4),(1,2),(2,4),(4,3)],5) => 2 ([(0,3),(1,4),(4,2)],5) => 3 ([(0,4),(3,2),(4,1),(4,3)],5) => 2 ([(0,4),(1,2),(2,3),(2,4)],5) => 2 ([(0,4),(2,3),(3,1),(4,2)],5) => 1 ([(0,3),(1,2),(2,4),(3,4)],5) => 1 ([(0,4),(1,2),(2,3),(3,4)],5) => 3 ([(0,3),(1,4),(2,4),(3,1),(3,2)],5) => 1 ([],6) => 120 ([(4,5)],6) => 120 ([(3,4),(3,5)],6) => 60 ([(2,3),(2,4),(2,5)],6) => 40 ([(1,2),(1,3),(1,4),(1,5)],6) => 30 ([(0,1),(0,2),(0,3),(0,4),(0,5)],6) => 24 ([(0,2),(0,3),(0,4),(0,5),(5,1)],6) => 24 ([(0,1),(0,2),(0,3),(0,4),(3,5),(4,5)],6) => 12 ([(0,1),(0,2),(0,3),(0,4),(2,5),(3,5),(4,5)],6) => 8 ([(0,1),(0,2),(0,3),(0,4),(1,5),(2,5),(3,5),(4,5)],6) => 6 ([(1,3),(1,4),(1,5),(5,2)],6) => 30 ([(0,3),(0,4),(0,5),(5,1),(5,2)],6) => 12 ([(1,2),(1,3),(1,4),(3,5),(4,5)],6) => 15 ([(1,2),(1,3),(1,4),(2,5),(3,5),(4,5)],6) => 10 ([(0,2),(0,3),(0,4),(2,5),(3,5),(4,5),(5,1)],6) => 2 ([(0,2),(0,3),(0,4),(2,5),(3,5),(4,1)],6) => 2 ([(0,1),(0,2),(0,3),(1,5),(2,4),(3,4),(3,5)],6) => 2 ([(0,1),(0,2),(0,3),(1,5),(2,4),(2,5),(3,4),(3,5)],6) => 2 ([(0,1),(0,2),(0,3),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6) => 2 ([(0,2),(0,3),(0,4),(2,5),(3,5),(4,1),(4,5)],6) => 2 ([(0,1),(0,2),(0,3),(1,5),(2,4),(3,4),(4,5)],6) => 3 ([(0,2),(0,3),(0,4),(3,5),(4,5),(5,1)],6) => 4 ([(0,3),(0,4),(0,5),(4,2),(5,1)],6) => 4 ([(0,2),(0,3),(0,4),(3,5),(4,1),(4,5)],6) => 4 ([(0,1),(0,2),(0,3),(2,4),(2,5),(3,4),(3,5)],6) => 4 ([(2,3),(2,4),(4,5)],6) => 40 ([(1,4),(1,5),(5,2),(5,3)],6) => 15 ([(0,4),(0,5),(5,1),(5,2),(5,3)],6) => 8 ([(2,3),(2,4),(3,5),(4,5)],6) => 20 ([(1,2),(1,3),(2,5),(3,5),(5,4)],6) => 5 ([(0,3),(0,4),(3,5),(4,5),(5,1),(5,2)],6) => 1 ([(1,4),(1,5),(4,3),(5,2)],6) => 5 ([(1,3),(1,4),(3,5),(4,2),(4,5)],6) => 5 ([(1,2),(1,3),(2,4),(2,5),(3,4),(3,5)],6) => 5 ([(0,2),(0,3),(2,4),(2,5),(3,4),(3,5),(5,1)],6) => 2 ([(0,1),(0,2),(1,4),(1,5),(2,4),(2,5),(4,3),(5,3)],6) => 1 ([(0,3),(0,4),(3,5),(4,1),(4,5),(5,2)],6) => 2 ([(0,4),(0,5),(4,3),(5,1),(5,2)],6) => 2 ([(0,3),(0,4),(3,5),(4,1),(4,2),(4,5)],6) => 2 ([(0,3),(0,4),(3,2),(3,5),(4,1),(4,5)],6) => 2 ([(0,2),(0,3),(2,4),(2,5),(3,1),(3,4),(3,5)],6) => 2 ([(0,1),(0,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5)],6) => 2 ([(3,4),(4,5)],6) => 60 ([(2,3),(3,4),(3,5)],6) => 20 ([(1,5),(5,2),(5,3),(5,4)],6) => 10 ([(0,5),(5,1),(5,2),(5,3),(5,4)],6) => 6 ([(2,3),(3,5),(5,4)],6) => 20 ([(1,4),(4,5),(5,2),(5,3)],6) => 5 ([(0,4),(4,5),(5,1),(5,2),(5,3)],6) => 2 ([(3,5),(4,5)],6) => 60 ([(2,5),(3,5),(5,4)],6) => 20 ([(1,5),(2,5),(5,3),(5,4)],6) => 5 ([(0,5),(1,5),(5,2),(5,3),(5,4)],6) => 2 ([(2,5),(3,5),(4,5)],6) => 40 ([(1,5),(2,5),(3,5),(5,4)],6) => 10 ([(0,5),(1,5),(2,5),(5,3),(5,4)],6) => 2 ([(1,5),(2,5),(3,5),(4,5)],6) => 30 ([(0,5),(1,5),(2,5),(3,5),(5,4)],6) => 6 ([(0,5),(1,5),(2,5),(3,5),(4,5)],6) => 24 ([(0,5),(1,5),(2,5),(3,4)],6) => 6 ([(0,5),(1,5),(2,5),(3,4),(5,3)],6) => 2 ([(0,5),(1,5),(2,5),(3,4),(5,4)],6) => 8 ([(0,5),(1,5),(2,5),(3,4),(3,5)],6) => 6 ([(0,5),(1,5),(2,5),(3,4),(4,5)],6) => 24 ([(1,5),(2,5),(3,4)],6) => 10 ([(1,5),(2,4),(3,4),(3,5)],6) => 10 ([(0,5),(1,4),(2,4),(2,5),(5,3)],6) => 5 ([(0,4),(1,3),(2,3),(2,4),(3,5),(4,5)],6) => 2 ([(1,5),(2,4),(2,5),(3,4),(3,5)],6) => 10 ([(0,5),(1,4),(1,5),(2,4),(2,5),(4,3)],6) => 5 ([(0,5),(1,3),(1,5),(2,3),(2,5),(3,4),(5,4)],6) => 2 ([(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6) => 10 ([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(5,3)],6) => 4 ([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(4,3),(5,3)],6) => 2 ([(0,5),(1,4),(1,5),(2,4),(2,5),(5,3)],6) => 4 ([(1,5),(2,5),(3,4),(5,3)],6) => 5 ([(1,5),(2,4),(3,4),(4,5)],6) => 15 ([(0,5),(1,4),(2,4),(4,5),(5,3)],6) => 3 ([(0,5),(1,5),(2,3),(5,4)],6) => 5 ([(0,5),(1,5),(4,2),(5,3),(5,4)],6) => 2 ([(0,5),(1,5),(2,4),(5,3),(5,4)],6) => 3 ([(1,5),(2,5),(3,4),(3,5)],6) => 10 ([(0,5),(1,5),(2,3),(2,5),(5,4)],6) => 4 ([(0,5),(1,5),(2,3),(2,5),(3,4)],6) => 8 ([(0,5),(1,5),(2,3),(2,5),(3,4),(5,4)],6) => 2 ([(0,5),(1,5),(2,3),(2,4)],6) => 4 ([(0,5),(1,5),(4,2),(4,3),(5,4)],6) => 1 ([(0,4),(1,4),(2,3),(2,5),(4,5)],6) => 5 ([(0,3),(1,3),(2,4),(2,5),(3,4),(3,5)],6) => 3 ([(0,5),(1,5),(2,3),(2,4),(2,5)],6) => 4 ([(0,5),(1,2),(1,4),(3,5),(4,3)],6) => 11 ([(0,3),(0,4),(1,5),(2,5),(4,1),(4,2)],6) => 4 ([(0,3),(0,4),(1,5),(2,5),(3,2),(4,1)],6) => 1 ([(0,5),(1,5),(2,3),(2,4),(4,5)],6) => 18 ([(0,5),(1,3),(1,4),(2,5),(3,5),(4,2)],6) => 8 ([(0,3),(0,4),(1,5),(2,5),(3,5),(4,1),(4,2)],6) => 3 ([(0,5),(1,5),(2,3),(2,4),(3,5),(4,5)],6) => 12 ([(1,5),(2,5),(3,4),(4,5)],6) => 30 ([(0,5),(1,5),(2,3),(3,5),(5,4)],6) => 6 ([(0,5),(1,5),(2,3),(3,4)],6) => 8 ([(0,5),(1,5),(3,2),(4,3),(5,4)],6) => 1 ([(0,4),(1,4),(2,3),(3,5),(4,5)],6) => 2 ([(0,5),(1,4),(3,5),(4,2),(4,3)],6) => 7 ([(0,4),(2,5),(3,5),(4,1),(4,2),(4,3)],6) => 3 ([(0,5),(1,5),(2,3),(3,4),(3,5)],6) => 6 ([(0,5),(1,5),(2,3),(3,4),(4,5)],6) => 12 ([(0,5),(1,4),(2,5),(3,5),(4,2),(4,3)],6) => 4 ([(0,4),(1,5),(2,5),(3,5),(4,1),(4,2),(4,3)],6) => 2 ([(0,5),(1,5),(2,4),(3,4)],6) => 6 ([(0,5),(1,5),(2,4),(3,4),(3,5)],6) => 6 ([(0,5),(1,5),(2,4),(2,5),(3,4),(3,5)],6) => 6 ([(0,5),(1,4),(2,4),(2,5),(3,4),(3,5)],6) => 6 ([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6) => 6 ([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6) => 6 ([(0,5),(1,4),(2,4),(3,5),(4,3)],6) => 4 ([(0,4),(1,4),(2,5),(3,5),(4,2),(4,3)],6) => 1 ([(0,5),(1,5),(2,4),(3,4),(4,5)],6) => 12 ([(2,5),(3,4)],6) => 20 ([(2,5),(3,4),(3,5)],6) => 20 ([(1,5),(2,3),(2,5),(3,4)],6) => 15 ([(0,5),(1,4),(1,5),(4,2),(4,3)],6) => 5 ([(0,4),(1,2),(1,4),(2,3),(2,5),(4,5)],6) => 1 ([(0,5),(1,2),(1,5),(2,3),(2,4),(5,3),(5,4)],6) => 1 ([(1,4),(2,3),(2,4),(3,5),(4,5)],6) => 5 ([(0,4),(1,2),(1,4),(2,5),(4,5),(5,3)],6) => 1 ([(0,5),(1,4),(1,5),(4,2),(5,3)],6) => 1 ([(0,4),(1,2),(1,4),(2,5),(4,3),(4,5)],6) => 1 ([(2,4),(2,5),(3,4),(3,5)],6) => 20 ([(1,4),(1,5),(2,4),(2,5),(5,3)],6) => 10 ([(0,4),(0,5),(1,4),(1,5),(5,2),(5,3)],6) => 3 ([(1,3),(1,4),(2,3),(2,4),(3,5),(4,5)],6) => 5 ([(0,4),(0,5),(1,4),(1,5),(4,3),(5,2)],6) => 1 ([(0,4),(0,5),(1,4),(1,5),(4,3),(5,2),(5,3)],6) => 1 ([(0,4),(0,5),(1,4),(1,5),(4,2),(4,3),(5,2),(5,3)],6) => 1 ([(0,4),(0,5),(1,4),(1,5),(2,3)],6) => 4 ([(0,4),(0,5),(1,4),(1,5),(2,3),(5,2)],6) => 3 ([(0,4),(0,5),(1,4),(1,5),(3,2),(4,3),(5,3)],6) => 1 ([(0,4),(0,5),(1,4),(1,5),(2,3),(4,2),(5,3)],6) => 2 ([(0,5),(1,3),(1,4),(2,3),(2,4),(4,5)],6) => 7 ([(0,5),(1,3),(1,4),(2,3),(2,4),(3,5),(4,5)],6) => 4 ([(0,4),(0,5),(1,4),(1,5),(2,3),(2,5)],6) => 4 ([(0,4),(0,5),(1,3),(1,5),(2,3),(2,5),(3,4)],6) => 5 ([(0,4),(0,5),(1,4),(1,5),(2,3),(2,4),(2,5)],6) => 4 ([(0,4),(0,5),(1,4),(1,5),(2,3),(2,4),(3,5)],6) => 8 ([(0,4),(0,5),(1,4),(1,5),(2,3),(3,5)],6) => 8 ([(0,4),(0,5),(1,4),(1,5),(2,3),(3,4),(3,5)],6) => 6 ([(1,5),(2,3),(2,5),(5,4)],6) => 10 ([(0,5),(1,2),(1,5),(5,3),(5,4)],6) => 3 ([(1,5),(2,3),(2,4)],6) => 10 ([(1,5),(2,3),(2,4),(2,5)],6) => 10 ([(0,5),(1,3),(1,4),(1,5),(4,2)],6) => 10 ([(0,4),(1,2),(1,3),(1,4),(3,5),(4,5)],6) => 3 ([(0,4),(1,2),(1,3),(1,4),(2,5),(3,5)],6) => 5 ([(0,4),(1,2),(1,3),(1,4),(2,5),(3,5),(4,5)],6) => 2 ([(0,5),(1,2),(1,3),(1,5),(5,4)],6) => 6 ([(0,5),(1,2),(1,3),(1,4)],6) => 6 ([(0,5),(1,2),(1,3),(1,4),(1,5)],6) => 6 ([(0,2),(0,3),(0,5),(4,1),(5,4)],6) => 12 ([(0,5),(1,2),(1,3),(1,4),(4,5)],6) => 18 ([(0,2),(0,3),(0,4),(1,5),(3,5),(4,1)],6) => 8 ([(0,5),(1,2),(1,3),(1,4),(3,5),(4,5)],6) => 11 ([(0,2),(0,3),(0,4),(1,5),(2,5),(3,5),(4,1)],6) => 6 ([(0,5),(1,2),(1,3),(1,4),(2,5),(3,5),(4,5)],6) => 8 ([(0,4),(1,2),(1,3),(1,5),(4,5)],6) => 8 ([(0,3),(1,2),(1,4),(1,5),(3,4),(3,5)],6) => 5 ([(0,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5)],6) => 4 ([(1,3),(1,5),(4,2),(5,4)],6) => 15 ([(0,3),(0,4),(4,5),(5,1),(5,2)],6) => 4 ([(0,4),(0,5),(3,2),(4,3),(5,1)],6) => 3 ([(0,2),(0,4),(2,5),(3,1),(4,3),(4,5)],6) => 3 ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6) => 1 ([(0,3),(0,4),(2,5),(3,2),(4,1),(4,5)],6) => 3 ([(0,2),(0,3),(1,4),(2,4),(2,5),(3,1),(3,5)],6) => 3 ([(1,5),(2,3),(2,4),(4,5)],6) => 25 ([(0,5),(1,2),(1,3),(3,5),(5,4)],6) => 7 ([(1,3),(1,4),(2,5),(3,5),(4,2)],6) => 10 ([(0,3),(0,4),(1,5),(3,5),(4,1),(5,2)],6) => 2 ([(1,5),(2,3),(2,4),(3,5),(4,5)],6) => 15 ([(0,5),(1,2),(1,3),(2,5),(3,5),(5,4)],6) => 3 ([(0,5),(1,3),(1,4),(3,5),(4,2)],6) => 3 ([(0,4),(1,2),(1,3),(2,5),(3,4),(3,5)],6) => 3 ([(0,5),(1,2),(1,3),(2,4),(2,5),(3,4),(3,5)],6) => 3 ([(0,4),(1,2),(1,3),(2,5),(3,4),(4,5)],6) => 5 ([(0,3),(0,4),(2,5),(3,5),(4,1),(4,2)],6) => 5 ([(0,5),(1,3),(1,4),(3,5),(4,2),(4,5)],6) => 3 ([(0,4),(1,3),(1,5),(5,2)],6) => 10 ([(0,3),(0,5),(4,2),(5,1),(5,4)],6) => 8 ([(0,5),(1,3),(1,4),(4,2),(4,5)],6) => 7 ([(0,4),(1,2),(1,3),(3,5),(4,5)],6) => 3 ([(0,2),(0,4),(1,5),(2,5),(3,1),(4,3)],6) => 3 ([(0,4),(1,2),(1,3),(2,5),(3,5)],6) => 5 ([(0,4),(1,2),(1,3),(2,5),(3,5),(4,5)],6) => 2 ([(0,2),(0,3),(2,5),(3,5),(4,1),(5,4)],6) => 1 ([(0,4),(1,2),(1,3),(2,5),(3,5),(5,4)],6) => 4 ([(1,4),(1,5),(2,3),(2,5)],6) => 10 ([(1,4),(1,5),(2,3),(2,4),(2,5)],6) => 10 ([(0,4),(0,5),(1,3),(1,4),(1,5),(5,2)],6) => 6 ([(0,4),(0,5),(1,2),(1,4),(1,5),(4,3),(5,3)],6) => 3 ([(1,3),(1,4),(1,5),(2,3),(2,4),(2,5)],6) => 10 ([(0,3),(0,4),(0,5),(1,3),(1,4),(1,5),(5,2)],6) => 6 ([(0,3),(0,4),(0,5),(1,3),(1,4),(1,5),(4,2),(5,2)],6) => 3 ([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,5),(3,5),(4,5)],6) => 2 ([(0,4),(0,5),(1,2),(1,4),(1,5),(2,3)],6) => 8 ([(0,4),(0,5),(1,2),(1,4),(1,5),(2,3),(5,3)],6) => 3 ([(0,3),(0,4),(1,2),(1,3),(1,4),(2,5),(3,5),(4,5)],6) => 2 ([(0,4),(0,5),(1,3),(1,5),(5,2)],6) => 6 ([(1,4),(1,5),(2,3),(2,4),(3,5)],6) => 15 ([(0,4),(0,5),(1,2),(1,4),(2,5),(4,3)],6) => 1 ([(0,4),(0,5),(1,2),(1,4),(2,5),(5,3)],6) => 5 ([(0,2),(0,5),(1,4),(1,5),(2,4),(4,3),(5,3)],6) => 3 ([(0,3),(0,5),(1,4),(1,5),(4,2)],6) => 8 ([(0,2),(0,4),(1,3),(1,4),(3,5),(4,5)],6) => 3 ([(0,4),(0,5),(1,2),(1,4),(2,3),(2,5)],6) => 5 ([(0,2),(0,5),(1,4),(1,5),(2,3),(2,4),(5,3)],6) => 1 ([(0,3),(0,4),(1,2),(1,4),(2,5),(3,5)],6) => 3 ([(0,3),(0,4),(1,2),(1,4),(2,5),(3,5),(4,5)],6) => 2 ([(0,4),(0,5),(1,2),(1,4),(2,3),(3,5)],6) => 6 ([(0,4),(0,5),(1,2),(1,3)],6) => 6 ([(0,4),(0,5),(1,2),(1,3),(1,5)],6) => 6 ([(0,4),(0,5),(1,2),(1,3),(1,4),(1,5)],6) => 6 ([(0,4),(0,5),(1,2),(1,3),(1,4),(3,5)],6) => 10 ([(0,4),(0,5),(1,2),(1,3),(1,4),(2,5),(3,5)],6) => 5 ([(0,3),(0,4),(0,5),(1,2),(1,4),(1,5)],6) => 6 ([(0,3),(0,4),(0,5),(1,2),(1,3),(1,4),(1,5)],6) => 6 ([(0,2),(0,3),(0,4),(0,5),(1,2),(1,3),(1,4),(1,5)],6) => 6 ([(0,2),(0,4),(0,5),(1,3),(1,4),(1,5),(2,3)],6) => 8 ([(0,3),(0,4),(1,2),(1,4),(1,5),(3,5)],6) => 8 ([(0,2),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4)],6) => 5 ([(0,4),(0,5),(1,2),(1,3),(3,5)],6) => 10 ([(0,4),(0,5),(1,2),(1,3),(3,4),(3,5)],6) => 7 ([(0,2),(0,3),(1,4),(1,5),(2,4),(2,5),(3,1)],6) => 2 ([(0,2),(0,4),(2,5),(3,1),(3,5),(4,3)],6) => 2 ([(0,4),(0,5),(1,2),(1,3),(2,5),(3,5)],6) => 5 ([(0,4),(0,5),(1,2),(1,3),(2,5),(3,4)],6) => 3 ([(0,4),(0,5),(1,2),(1,3),(2,5),(3,4),(3,5)],6) => 3 ([(0,4),(0,5),(1,2),(1,3),(2,4),(2,5),(3,4),(3,5)],6) => 3 ([(0,3),(0,5),(1,2),(1,4),(2,5),(3,4)],6) => 1 ([(1,4),(2,3),(2,5),(4,5)],6) => 15 ([(0,4),(1,3),(1,5),(4,5),(5,2)],6) => 5 ([(1,4),(1,5),(2,3),(3,4),(3,5)],6) => 10 ([(0,4),(0,5),(1,3),(3,4),(3,5),(5,2)],6) => 4 ([(0,2),(1,4),(1,5),(2,4),(2,5),(4,3),(5,3)],6) => 2 ([(0,3),(1,4),(1,5),(3,5),(4,2)],6) => 1 ([(0,3),(1,2),(1,4),(2,5),(3,4),(4,5)],6) => 3 ([(0,3),(1,2),(1,4),(2,5),(3,4),(3,5)],6) => 1 ([(0,5),(1,3),(1,4),(5,2)],6) => 8 ([(0,2),(0,5),(3,4),(4,1),(5,3)],6) => 4 ([(0,5),(4,2),(4,3),(5,1),(5,4)],6) => 3 ([(0,4),(1,3),(1,5),(4,2),(4,5)],6) => 5 ([(0,4),(0,5),(1,2),(2,3),(2,4),(2,5)],6) => 4 ([(0,4),(0,5),(1,2),(2,3),(2,5),(3,4)],6) => 5 ([(2,5),(3,4),(4,5)],6) => 40 ([(1,5),(2,3),(3,5),(5,4)],6) => 10 ([(0,5),(1,2),(2,5),(5,3),(5,4)],6) => 2 ([(1,3),(2,4),(4,5)],6) => 15 ([(1,5),(4,3),(5,2),(5,4)],6) => 10 ([(1,5),(2,3),(3,4),(3,5)],6) => 10 ([(0,5),(1,4),(4,2),(4,5),(5,3)],6) => 4 ([(0,4),(1,5),(5,2),(5,3)],6) => 5 ([(0,5),(4,3),(5,1),(5,2),(5,4)],6) => 6 ([(0,5),(1,4),(4,2),(4,3),(4,5)],6) => 4 ([(1,5),(3,4),(4,2),(5,3)],6) => 5 ([(0,4),(3,5),(4,3),(5,1),(5,2)],6) => 1 ([(1,4),(2,3),(3,5),(4,5)],6) => 5 ([(0,4),(1,3),(3,5),(4,5),(5,2)],6) => 1 ([(0,5),(1,4),(4,2),(5,3)],6) => 1 ([(0,5),(3,4),(4,2),(5,1),(5,3)],6) => 3 ([(0,3),(1,4),(3,5),(4,2),(4,5)],6) => 1 ([(0,3),(1,2),(2,4),(2,5),(3,4),(3,5)],6) => 1 ([(1,5),(2,3),(3,4),(4,5)],6) => 15 ([(1,4),(2,5),(3,5),(4,2),(4,3)],6) => 5 ([(0,4),(1,5),(2,5),(4,1),(4,2),(5,3)],6) => 1 ([(0,5),(1,4),(2,5),(4,2),(5,3)],6) => 3 ([(0,5),(1,4),(2,3)],6) => 4 ([(0,5),(1,3),(2,4),(2,5)],6) => 4 ([(0,5),(1,4),(2,3),(2,4),(2,5)],6) => 4 ([(0,5),(1,4),(1,5),(3,2),(4,3)],6) => 6 ([(0,4),(1,2),(1,4),(2,3),(3,5),(4,5)],6) => 3 ([(0,5),(1,4),(2,3),(2,4),(3,5)],6) => 10 ([(0,4),(1,2),(1,4),(2,5),(3,5),(4,3)],6) => 2 ([(0,5),(1,4),(2,3),(2,4),(3,5),(4,5)],6) => 4 ([(0,5),(1,3),(1,5),(4,2),(5,4)],6) => 3 ([(0,5),(1,4),(2,3),(2,4),(4,5)],6) => 7 ([(0,4),(1,4),(1,5),(2,3),(2,5)],6) => 4 ([(0,3),(1,4),(1,5),(2,3),(2,4),(2,5)],6) => 4 ([(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5)],6) => 4 ([(0,4),(0,5),(1,3),(1,5),(2,3),(2,4)],6) => 4 ([(0,4),(0,5),(1,3),(1,5),(2,3),(2,4),(2,5)],6) => 4 ([(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5)],6) => 4 ([(0,3),(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5)],6) => 4 ([(0,4),(1,3),(1,5),(2,3),(2,4),(4,5)],6) => 5 ([(0,5),(1,4),(1,5),(2,3),(2,4),(2,5)],6) => 4 ([(0,5),(1,4),(1,5),(2,3),(2,4),(3,5)],6) => 10 ([(0,5),(1,4),(1,5),(2,3),(2,5)],6) => 4 ([(0,5),(1,4),(1,5),(2,3),(2,5),(3,4)],6) => 8 ([(0,4),(1,4),(1,5),(2,3),(3,5)],6) => 8 ([(0,5),(1,4),(1,5),(2,3),(3,4),(3,5)],6) => 6 ([(0,4),(1,3),(1,5),(2,5),(4,2)],6) => 6 ([(0,4),(0,5),(1,2),(2,3),(3,4),(3,5)],6) => 3 ([(0,3),(1,4),(1,5),(2,4),(2,5),(3,1),(3,2)],6) => 1 ([(0,4),(2,5),(3,1),(3,5),(4,2),(4,3)],6) => 1 ([(0,5),(1,4),(2,3),(2,5),(4,5)],6) => 10 ([(0,5),(1,3),(4,2),(5,4)],6) => 6 ([(0,5),(3,2),(4,1),(5,3),(5,4)],6) => 1 ([(0,5),(1,4),(3,2),(4,3),(4,5)],6) => 5 ([(0,5),(1,2),(2,3),(2,5),(3,4),(5,4)],6) => 2 ([(0,4),(3,2),(4,5),(5,1),(5,3)],6) => 2 ([(0,5),(1,3),(3,4),(4,2),(4,5)],6) => 3 ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => 1 ([(0,5),(1,3),(2,4),(4,5)],6) => 10 ([(0,5),(1,4),(2,3),(3,4),(3,5)],6) => 6 ([(0,5),(1,3),(3,5),(4,2),(5,4)],6) => 2 ([(0,5),(1,4),(2,3),(3,5),(5,4)],6) => 8 ([(0,5),(1,4),(2,5),(3,2),(4,3)],6) => 4 ([(0,3),(1,5),(2,5),(3,4),(4,1),(4,2)],6) => 1 ([(0,3),(1,4),(2,5),(3,5),(4,2)],6) => 3 ([(0,4),(1,5),(2,5),(3,2),(4,1),(4,3)],6) => 2 ([(0,5),(1,4),(2,3),(3,5),(4,5)],6) => 4 ([],7) => 720 ([(5,6)],7) => 720 ([(4,5),(4,6)],7) => 360 ([(3,4),(3,5),(3,6)],7) => 240 ([(2,3),(2,4),(2,5),(2,6)],7) => 180 ([(1,2),(1,3),(1,4),(1,5),(1,6)],7) => 144 ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6)],7) => 120 ([(0,2),(0,3),(0,4),(0,5),(0,6),(6,1)],7) => 120 ([(0,1),(0,2),(0,3),(0,4),(0,5),(4,6),(5,6)],7) => 60 ([(0,1),(0,2),(0,3),(0,4),(0,5),(3,6),(4,6),(5,6)],7) => 40 ([(0,1),(0,2),(0,3),(0,4),(0,5),(2,6),(3,6),(4,6),(5,6)],7) => 30 ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 24 ([(1,3),(1,4),(1,5),(1,6),(6,2)],7) => 144 ([(0,3),(0,4),(0,5),(0,6),(6,1),(6,2)],7) => 60 ([(1,2),(1,3),(1,4),(1,5),(4,6),(5,6)],7) => 72 ([(1,2),(1,3),(1,4),(1,5),(3,6),(4,6),(5,6)],7) => 48 ([(1,2),(1,3),(1,4),(1,5),(2,6),(3,6),(4,6),(5,6)],7) => 36 ([(0,2),(0,3),(0,4),(0,5),(2,6),(3,6),(4,6),(5,6),(6,1)],7) => 6 ([(0,2),(0,3),(0,4),(0,5),(2,6),(3,6),(4,6),(5,1)],7) => 6 ([(0,2),(0,3),(0,4),(0,5),(2,6),(3,6),(4,6),(5,1),(5,6)],7) => 6 ([(0,1),(0,2),(0,3),(0,4),(1,6),(2,6),(3,6),(4,5),(6,5)],7) => 8 ([(0,2),(0,3),(0,4),(0,5),(3,6),(4,6),(5,6),(6,1)],7) => 10 ([(0,2),(0,3),(0,4),(0,5),(3,6),(4,6),(5,1)],7) => 10 ([(0,1),(0,2),(0,3),(0,4),(2,6),(3,5),(4,5),(4,6)],7) => 10 ([(0,1),(0,2),(0,3),(0,4),(2,6),(3,5),(3,6),(4,5),(4,6)],7) => 10 ([(0,1),(0,2),(0,3),(0,4),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6)],7) => 10 ([(0,2),(0,3),(0,4),(0,5),(3,6),(4,6),(5,1),(5,6)],7) => 10 ([(0,1),(0,2),(0,3),(0,4),(1,6),(2,6),(3,5),(4,5)],7) => 6 ([(0,1),(0,2),(0,3),(0,4),(1,6),(2,6),(3,5),(4,5),(4,6)],7) => 6 ([(0,1),(0,2),(0,3),(0,4),(1,6),(2,6),(3,5),(3,6),(4,5),(4,6)],7) => 6 ([(0,1),(0,2),(0,3),(0,4),(1,6),(2,5),(3,5),(3,6),(4,5),(4,6)],7) => 6 ([(0,1),(0,2),(0,3),(0,4),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6)],7) => 6 ([(0,1),(0,2),(0,3),(0,4),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6)],7) => 6 ([(0,1),(0,2),(0,3),(0,4),(1,6),(2,6),(3,5),(4,5),(5,6)],7) => 12 ([(0,1),(0,2),(0,3),(0,4),(2,6),(3,5),(4,5),(5,6)],7) => 15 ([(0,2),(0,3),(0,4),(0,5),(4,6),(5,6),(6,1)],7) => 20 ([(0,3),(0,4),(0,5),(0,6),(5,2),(6,1)],7) => 20 ([(0,2),(0,3),(0,4),(0,5),(4,6),(5,1),(5,6)],7) => 20 ([(0,1),(0,2),(0,3),(0,4),(3,5),(3,6),(4,5),(4,6)],7) => 20 ([(2,4),(2,5),(2,6),(6,3)],7) => 180 ([(1,4),(1,5),(1,6),(6,2),(6,3)],7) => 72 ([(0,4),(0,5),(0,6),(6,1),(6,2),(6,3)],7) => 40 ([(2,3),(2,4),(2,5),(4,6),(5,6)],7) => 90 ([(2,3),(2,4),(2,5),(3,6),(4,6),(5,6)],7) => 60 ([(1,2),(1,3),(1,4),(2,6),(3,6),(4,6),(6,5)],7) => 12 ([(0,3),(0,4),(0,5),(3,6),(4,6),(5,6),(6,1),(6,2)],7) => 2 ([(1,3),(1,4),(1,5),(3,6),(4,6),(5,2)],7) => 12 ([(1,2),(1,3),(1,4),(2,6),(3,5),(4,5),(4,6)],7) => 12 ([(1,2),(1,3),(1,4),(2,6),(3,5),(3,6),(4,5),(4,6)],7) => 12 ([(1,2),(1,3),(1,4),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6)],7) => 12 ([(0,2),(0,3),(0,4),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(6,1)],7) => 4 ([(0,1),(0,2),(0,3),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(5,4),(6,4)],7) => 2 ([(0,2),(0,3),(0,4),(2,6),(3,5),(3,6),(4,5),(4,6),(5,1)],7) => 5 ([(0,1),(0,2),(0,3),(1,6),(2,4),(2,6),(3,4),(3,6),(4,5),(6,5)],7) => 2 ([(0,2),(0,3),(0,4),(2,6),(3,5),(3,6),(4,5),(4,6),(6,1)],7) => 4 ([(0,2),(0,3),(0,4),(2,6),(3,5),(4,5),(4,6),(6,1)],7) => 5 ([(0,1),(0,2),(0,3),(1,5),(2,4),(3,4),(3,5),(4,6),(5,6)],7) => 2 ([(1,3),(1,4),(1,5),(3,6),(4,6),(5,2),(5,6)],7) => 12 ([(0,3),(0,4),(0,5),(3,6),(4,6),(5,1),(5,6),(6,2)],7) => 4 ([(0,3),(0,4),(0,5),(3,6),(4,6),(5,1),(5,2)],7) => 4 ([(0,3),(0,4),(0,5),(3,6),(4,6),(5,1),(5,2),(5,6)],7) => 4 ([(0,2),(0,3),(0,4),(2,5),(3,5),(4,1),(4,6),(5,6)],7) => 5 ([(0,1),(0,2),(0,3),(1,4),(2,4),(3,5),(3,6),(4,5),(4,6)],7) => 3 ([(1,2),(1,3),(1,4),(2,6),(3,5),(4,5),(5,6)],7) => 18 ([(0,2),(0,3),(0,4),(2,6),(3,5),(4,5),(5,6),(6,1)],7) => 3 ([(0,3),(0,4),(0,5),(3,6),(4,6),(5,1),(6,2)],7) => 5 ([(0,2),(0,3),(0,4),(2,6),(3,6),(4,5),(6,1),(6,5)],7) => 3 ([(1,2),(1,3),(1,4),(3,6),(4,6),(6,5)],7) => 24 ([(0,3),(0,4),(0,5),(4,6),(5,6),(6,1),(6,2)],7) => 5 ([(1,4),(1,5),(1,6),(5,3),(6,2)],7) => 24 ([(1,3),(1,4),(1,5),(4,6),(5,2),(5,6)],7) => 24 ([(1,2),(1,3),(1,4),(3,5),(3,6),(4,5),(4,6)],7) => 24 ([(0,2),(0,3),(0,4),(2,5),(2,6),(3,5),(3,6),(4,1)],7) => 4 ([(0,2),(0,3),(0,4),(2,5),(2,6),(3,5),(3,6),(4,1),(4,6)],7) => 4 ([(0,2),(0,3),(0,4),(2,5),(2,6),(3,5),(3,6),(4,1),(4,5),(4,6)],7) => 4 ([(0,1),(0,2),(0,3),(1,5),(1,6),(2,4),(2,6),(3,4),(3,6),(4,5)],7) => 5 ([(0,1),(0,2),(0,3),(1,6),(2,4),(2,5),(3,4),(3,5),(5,6)],7) => 7 ([(0,1),(0,2),(0,3),(1,6),(2,4),(2,5),(3,4),(3,5),(4,6),(5,6)],7) => 4 ([(0,2),(0,3),(0,4),(3,5),(3,6),(4,5),(4,6),(6,1)],7) => 10 ([(0,1),(0,2),(0,3),(2,4),(2,5),(3,4),(3,5),(4,6),(5,6)],7) => 5 ([(0,3),(0,4),(0,5),(4,6),(5,1),(5,6),(6,2)],7) => 10 ([(0,4),(0,5),(0,6),(5,3),(6,1),(6,2)],7) => 10 ([(0,3),(0,4),(0,5),(4,6),(5,1),(5,2),(5,6)],7) => 10 ([(0,3),(0,4),(0,5),(4,2),(4,6),(5,1),(5,6)],7) => 10 ([(0,2),(0,3),(0,4),(3,5),(3,6),(4,1),(4,5),(4,6)],7) => 10 ([(0,1),(0,2),(0,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6)],7) => 10 ([(0,4),(0,5),(0,6),(4,3),(5,2),(6,1)],7) => 4 ([(0,3),(0,4),(0,5),(3,6),(4,2),(5,1),(5,6)],7) => 4 ([(0,2),(0,3),(0,4),(2,6),(3,5),(4,1),(4,5),(4,6)],7) => 4 ([(0,2),(0,3),(0,4),(2,5),(3,5),(3,6),(4,1),(4,6)],7) => 4 ([(0,1),(0,2),(0,3),(1,4),(2,5),(2,6),(3,4),(3,5),(3,6)],7) => 4 ([(0,1),(0,2),(0,3),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6)],7) => 4 ([(0,1),(0,2),(0,3),(1,5),(1,6),(2,4),(2,6),(3,4),(3,5)],7) => 4 ([(0,1),(0,2),(0,3),(1,5),(1,6),(2,4),(2,6),(3,4),(3,5),(3,6)],7) => 4 ([(0,1),(0,2),(0,3),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6)],7) => 4 ([(0,1),(0,2),(0,3),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6)],7) => 4 ([(0,2),(0,3),(0,4),(2,6),(3,5),(3,6),(4,1),(4,5),(4,6)],7) => 4 ([(0,1),(0,2),(0,3),(1,5),(2,4),(2,6),(3,4),(3,5),(5,6)],7) => 5 ([(0,3),(0,4),(0,5),(3,6),(4,2),(4,6),(5,1),(5,6)],7) => 4 ([(0,2),(0,3),(0,4),(2,6),(3,5),(4,1),(4,5),(5,6)],7) => 7 ([(3,4),(3,5),(5,6)],7) => 240 ([(2,5),(2,6),(6,3),(6,4)],7) => 90 ([(1,5),(1,6),(6,2),(6,3),(6,4)],7) => 48 ([(0,5),(0,6),(6,1),(6,2),(6,3),(6,4)],7) => 30 ([(3,4),(3,5),(4,6),(5,6)],7) => 120 ([(2,3),(2,4),(3,6),(4,6),(6,5)],7) => 30 ([(1,2),(1,3),(2,6),(3,6),(6,4),(6,5)],7) => 6 ([(0,4),(0,5),(4,6),(5,6),(6,1),(6,2),(6,3)],7) => 2 ([(2,5),(2,6),(5,4),(6,3)],7) => 30 ([(2,3),(2,4),(3,6),(4,5),(4,6)],7) => 30 ([(2,3),(2,4),(3,5),(3,6),(4,5),(4,6)],7) => 30 ([(1,3),(1,4),(3,5),(3,6),(4,5),(4,6),(6,2)],7) => 12 ([(0,3),(0,4),(3,5),(3,6),(4,5),(4,6),(6,1),(6,2)],7) => 3 ([(1,2),(1,3),(2,5),(2,6),(3,5),(3,6),(5,4),(6,4)],7) => 6 ([(0,2),(0,3),(2,4),(2,5),(3,4),(3,5),(4,6),(5,6),(6,1)],7) => 1 ([(0,3),(0,4),(3,5),(3,6),(4,5),(4,6),(5,2),(6,1)],7) => 1 ([(0,2),(0,3),(2,4),(2,6),(3,4),(3,6),(4,5),(6,1),(6,5)],7) => 1 ([(0,1),(0,2),(1,5),(1,6),(2,5),(2,6),(5,3),(5,4),(6,3),(6,4)],7) => 1 ([(1,3),(1,5),(3,6),(5,2),(5,6),(6,4)],7) => 12 ([(0,4),(0,5),(4,6),(5,1),(5,6),(6,2),(6,3)],7) => 3 ([(1,5),(1,6),(5,4),(6,2),(6,3)],7) => 12 ([(1,4),(1,5),(4,6),(5,2),(5,3),(5,6)],7) => 12 ([(0,4),(0,5),(4,6),(5,1),(5,2),(5,6),(6,3)],7) => 6 ([(0,5),(0,6),(5,4),(6,1),(6,2),(6,3)],7) => 6 ([(0,4),(0,5),(4,6),(5,1),(5,2),(5,3),(5,6)],7) => 6 ([(1,4),(1,5),(4,3),(4,6),(5,2),(5,6)],7) => 12 ([(1,3),(1,4),(3,5),(3,6),(4,2),(4,5),(4,6)],7) => 12 ([(1,2),(1,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6)],7) => 12 ([(0,2),(0,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(6,1)],7) => 6 ([(0,1),(0,2),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(5,3),(6,3)],7) => 3 ([(0,1),(0,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,6),(4,6),(5,6)],7) => 2 ([(0,3),(0,4),(3,5),(3,6),(4,2),(4,5),(4,6),(6,1)],7) => 6 ([(0,2),(0,3),(2,4),(2,5),(3,1),(3,4),(3,5),(4,6),(5,6)],7) => 3 ([(0,4),(0,5),(4,2),(4,6),(5,1),(5,6),(6,3)],7) => 6 ([(0,5),(0,6),(5,3),(5,4),(6,1),(6,2)],7) => 6 ([(0,4),(0,5),(4,3),(4,6),(5,1),(5,2),(5,6)],7) => 6 ([(0,3),(0,4),(3,5),(3,6),(4,1),(4,2),(4,5),(4,6)],7) => 6 ([(0,3),(0,4),(3,2),(3,5),(3,6),(4,1),(4,5),(4,6)],7) => 6 ([(0,2),(0,3),(2,4),(2,5),(2,6),(3,1),(3,4),(3,5),(3,6)],7) => 6 ([(0,1),(0,2),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6)],7) => 6 ([(2,3),(2,4),(3,5),(4,6),(5,6)],7) => 60 ([(1,3),(1,5),(2,6),(3,6),(5,2),(6,4)],7) => 12 ([(0,4),(0,5),(1,6),(4,6),(5,1),(6,2),(6,3)],7) => 2 ([(4,5),(5,6)],7) => 360 ([(3,4),(4,5),(4,6)],7) => 120 ([(2,6),(6,3),(6,4),(6,5)],7) => 60 ([(1,6),(6,2),(6,3),(6,4),(6,5)],7) => 36 ([(0,6),(6,1),(6,2),(6,3),(6,4),(6,5)],7) => 24 ([(3,4),(4,6),(6,5)],7) => 120 ([(2,5),(5,6),(6,3),(6,4)],7) => 30 ([(1,5),(5,6),(6,2),(6,3),(6,4)],7) => 12 ([(0,5),(5,6),(6,1),(6,2),(6,3),(6,4)],7) => 6 ([(4,6),(5,6)],7) => 360 ([(3,6),(4,6),(6,5)],7) => 120 ([(2,6),(3,6),(6,4),(6,5)],7) => 30 ([(1,6),(2,6),(6,3),(6,4),(6,5)],7) => 12 ([(0,6),(1,6),(6,2),(6,3),(6,4),(6,5)],7) => 6 ([(3,6),(4,6),(5,6)],7) => 240 ([(2,6),(3,6),(4,6),(6,5)],7) => 60 ([(1,6),(2,6),(3,6),(6,4),(6,5)],7) => 12 ([(0,6),(1,6),(2,6),(6,3),(6,4),(6,5)],7) => 4 ([(2,6),(3,6),(4,6),(5,6)],7) => 180 ([(1,6),(2,6),(3,6),(4,6),(6,5)],7) => 36 ([(0,6),(1,6),(2,6),(3,6),(6,4),(6,5)],7) => 6 ([(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 144 ([(0,6),(1,6),(2,6),(3,6),(4,6),(6,5)],7) => 24 ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 120 ([(0,6),(1,6),(2,6),(3,6),(4,5)],7) => 24 ([(0,6),(1,6),(2,6),(3,6),(4,5),(6,4)],7) => 6 ([(0,6),(1,6),(2,6),(3,6),(4,5),(6,5)],7) => 30 ([(0,6),(1,6),(2,6),(3,6),(4,5),(4,6)],7) => 24 ([(0,6),(1,6),(2,6),(3,6),(4,5),(5,6)],7) => 120 ([(1,6),(2,6),(3,6),(4,5)],7) => 36 ([(1,6),(2,6),(3,6),(4,5),(6,4)],7) => 12 ([(1,6),(2,6),(3,6),(4,5),(6,5)],7) => 48 ([(0,6),(1,6),(2,6),(3,4),(6,5)],7) => 14 ([(0,6),(1,6),(2,6),(4,5),(6,3),(6,4)],7) => 4 ([(0,6),(1,6),(2,6),(3,5),(6,4),(6,5)],7) => 8 ([(1,6),(2,6),(3,6),(4,5),(4,6)],7) => 36 ([(0,6),(1,6),(2,6),(3,4),(3,6),(6,5)],7) => 12 ([(0,6),(1,6),(2,6),(3,4),(3,6),(4,5)],7) => 30 ([(0,6),(1,6),(2,6),(3,4),(3,6),(4,5),(6,5)],7) => 6 ([(0,6),(1,6),(2,6),(3,4),(3,5)],7) => 12 ([(0,6),(1,6),(2,6),(3,4),(3,5),(6,3)],7) => 2 ([(0,6),(1,6),(2,6),(3,4),(3,5),(6,5)],7) => 14 ([(0,6),(1,6),(2,6),(3,4),(3,5),(6,4),(6,5)],7) => 8 ([(0,6),(1,6),(2,6),(3,4),(3,5),(3,6)],7) => 12 ([(0,6),(1,6),(2,6),(3,4),(3,5),(5,6)],7) => 84 ([(0,6),(1,6),(2,6),(3,4),(3,5),(4,6),(5,6)],7) => 60 ([(1,6),(2,6),(3,6),(4,5),(5,6)],7) => 144 ([(0,6),(1,6),(2,6),(3,4),(4,6),(6,5)],7) => 24 ([(0,6),(1,6),(2,6),(3,4),(4,5)],7) => 30 ([(0,6),(1,6),(2,6),(3,5),(5,4),(6,3)],7) => 2 ([(0,6),(1,6),(2,6),(3,5),(5,4),(6,5)],7) => 8 ([(0,6),(1,6),(2,6),(3,4),(4,5),(6,5)],7) => 6 ([(0,6),(1,6),(2,6),(3,4),(4,5),(4,6)],7) => 24 ([(0,3),(1,6),(2,6),(3,5),(4,6),(5,4)],7) => 20 ([(0,6),(1,4),(2,6),(3,6),(4,5),(5,2),(5,3)],7) => 5 ([(0,4),(1,6),(2,6),(3,6),(4,5),(5,1),(5,2),(5,3)],7) => 2 ([(0,6),(1,6),(2,6),(3,4),(4,5),(5,6)],7) => 60 ([(0,6),(1,6),(2,6),(3,5),(4,5)],7) => 24 ([(0,6),(1,6),(2,5),(3,5),(4,5),(4,6)],7) => 24 ([(0,6),(1,6),(2,5),(3,5),(3,6),(4,5),(4,6)],7) => 24 ([(0,6),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6)],7) => 24 ([(0,6),(1,5),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6)],7) => 24 ([(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6)],7) => 24 ([(0,5),(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6)],7) => 24 ([(0,6),(1,6),(2,6),(3,5),(4,5),(6,4)],7) => 10 ([(0,6),(1,6),(2,6),(3,5),(4,5),(6,3),(6,4)],7) => 2 ([(0,6),(1,6),(2,5),(3,5),(4,5),(5,6)],7) => 40 ([(0,6),(1,6),(2,6),(3,5),(4,5),(4,6)],7) => 24 ([(0,6),(1,6),(2,6),(3,5),(3,6),(4,5),(4,6)],7) => 24 ([(0,6),(1,6),(2,5),(3,5),(4,6),(5,4)],7) => 20 ([(0,6),(1,5),(2,5),(3,6),(4,6),(5,3),(5,4)],7) => 5 ([(0,5),(1,5),(2,6),(3,6),(4,6),(5,2),(5,3),(5,4)],7) => 2 ([(0,6),(1,6),(2,6),(3,5),(4,5),(5,6)],7) => 60 ([(2,6),(3,6),(4,5)],7) => 60 ([(2,6),(3,5),(4,5),(4,6)],7) => 60 ([(1,6),(2,5),(3,5),(3,6),(6,4)],7) => 30 ([(0,6),(1,5),(2,5),(2,6),(6,3),(6,4)],7) => 8 ([(1,5),(2,4),(3,4),(3,5),(4,6),(5,6)],7) => 12 ([(0,5),(1,4),(2,4),(2,5),(4,6),(5,6),(6,3)],7) => 2 ([(0,6),(1,5),(2,5),(2,6),(5,3),(6,4)],7) => 2 ([(0,6),(1,4),(2,4),(2,6),(4,5),(6,3),(6,5)],7) => 2 ([(0,6),(1,5),(2,5),(2,6),(5,3),(5,4),(6,3),(6,4)],7) => 2 ([(2,6),(3,5),(3,6),(4,5),(4,6)],7) => 60 ([(1,6),(2,5),(2,6),(3,5),(3,6),(5,4)],7) => 30 ([(0,6),(1,5),(1,6),(2,5),(2,6),(5,3),(5,4)],7) => 8 ([(0,6),(1,5),(1,6),(2,5),(2,6),(5,3),(5,4),(6,4)],7) => 2 ([(0,6),(1,3),(1,6),(2,3),(2,6),(3,4),(3,5),(6,4),(6,5)],7) => 2 ([(1,6),(2,4),(2,6),(3,4),(3,6),(4,5),(6,5)],7) => 12 ([(0,6),(1,5),(1,6),(2,5),(2,6),(5,4),(6,3)],7) => 2 ([(0,6),(1,4),(1,6),(2,4),(2,6),(4,5),(6,3),(6,5)],7) => 2 ([(2,5),(2,6),(3,5),(3,6),(4,5),(4,6)],7) => 60 ([(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(6,4)],7) => 24 ([(0,5),(0,6),(1,5),(1,6),(2,5),(2,6),(6,3),(6,4)],7) => 6 ([(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(5,4),(6,4)],7) => 12 ([(0,5),(0,6),(1,5),(1,6),(2,5),(2,6),(5,4),(6,3)],7) => 2 ([(0,5),(0,6),(1,5),(1,6),(2,5),(2,6),(5,4),(6,3),(6,4)],7) => 2 ([(0,5),(0,6),(1,5),(1,6),(2,5),(2,6),(5,3),(5,4),(6,3),(6,4)],7) => 2 ([(0,5),(0,6),(1,5),(1,6),(2,5),(2,6),(3,4)],7) => 12 ([(0,5),(0,6),(1,5),(1,6),(2,5),(2,6),(3,4),(6,3)],7) => 6 ([(0,5),(0,6),(1,5),(1,6),(2,5),(2,6),(4,3),(5,4),(6,4)],7) => 2 ([(0,5),(0,6),(1,5),(1,6),(2,5),(2,6),(3,4),(6,4)],7) => 18 ([(0,5),(0,6),(1,5),(1,6),(2,5),(2,6),(3,4),(5,4),(6,3)],7) => 4 ([(0,6),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,6),(5,6)],7) => 10 ([(0,5),(0,6),(1,5),(1,6),(2,5),(2,6),(3,4),(3,6)],7) => 12 ([(0,5),(0,6),(1,5),(1,6),(2,5),(2,6),(3,4),(3,6),(5,4)],7) => 14 ([(0,5),(0,6),(1,5),(1,6),(2,5),(2,6),(3,4),(3,5),(3,6)],7) => 12 ([(0,5),(0,6),(1,5),(1,6),(2,5),(2,6),(3,4),(3,5),(4,6)],7) => 30 ([(0,5),(0,6),(1,5),(1,6),(2,5),(2,6),(3,4),(4,6)],7) => 30 ([(0,5),(0,6),(1,5),(1,6),(2,5),(2,6),(3,4),(4,5),(4,6)],7) => 24 ([(1,6),(2,5),(2,6),(3,5),(3,6),(6,4)],7) => 24 ([(0,6),(1,5),(1,6),(2,5),(2,6),(6,3),(6,4)],7) => 6 ([(0,6),(1,5),(1,6),(2,5),(2,6),(3,4)],7) => 12 ([(0,6),(1,5),(1,6),(2,5),(2,6),(3,4),(5,3)],7) => 9 ([(0,6),(1,4),(1,6),(2,4),(2,6),(4,5),(5,3),(6,5)],7) => 2 ([(0,6),(1,4),(1,6),(2,4),(2,6),(3,5),(4,3),(6,5)],7) => 5 ([(0,5),(1,6),(2,4),(2,6),(3,4),(3,6),(4,5)],7) => 22 ([(0,6),(1,4),(1,6),(2,4),(2,6),(3,5),(4,5),(6,3)],7) => 4 ([(0,6),(1,5),(2,4),(2,5),(3,4),(3,5),(4,6),(5,6)],7) => 10 ([(0,6),(1,5),(1,6),(2,5),(2,6),(3,4),(6,3)],7) => 6 ([(0,6),(1,5),(2,4),(2,6),(3,4),(3,6),(6,5)],7) => 18 ([(0,5),(1,5),(1,6),(2,5),(2,6),(3,4),(3,6)],7) => 12 ([(0,6),(1,5),(1,6),(2,5),(2,6),(3,4),(3,5),(6,4)],7) => 14 ([(0,6),(1,5),(1,6),(2,5),(2,6),(3,4),(3,5),(3,6)],7) => 12 ([(0,6),(1,5),(1,6),(2,5),(2,6),(3,4),(3,5),(4,6)],7) => 34 ([(0,6),(1,5),(1,6),(2,5),(2,6),(3,4),(3,6)],7) => 12 ([(0,6),(1,5),(1,6),(2,4),(2,6),(3,4),(3,6),(4,5)],7) => 18 ([(0,6),(1,5),(1,6),(2,5),(2,6),(3,4),(3,6),(4,5)],7) => 30 ([(0,5),(1,5),(1,6),(2,5),(2,6),(3,4),(4,6)],7) => 30 ([(0,6),(1,5),(1,6),(2,5),(2,6),(3,4),(4,5),(4,6)],7) => 24 ([(0,6),(1,5),(1,6),(2,5),(2,6),(3,4),(4,6)],7) => 34 ([(0,6),(1,5),(2,5),(2,6),(3,4)],7) => 12 ([(0,6),(1,5),(2,4),(3,4),(3,5),(3,6)],7) => 12 ([(0,6),(1,5),(2,5),(2,6),(3,4),(6,3)],7) => 9 ([(0,6),(1,4),(2,5),(3,4),(3,5),(5,6)],7) => 22 ([(0,5),(1,4),(2,4),(2,5),(3,6),(4,6),(5,3)],7) => 5 ([(0,6),(1,5),(2,4),(3,4),(3,5),(4,6),(5,6)],7) => 10 ([(0,6),(1,5),(2,5),(2,6),(3,4),(3,6)],7) => 12 ([(0,6),(1,5),(1,6),(2,4),(2,6),(3,4),(3,5)],7) => 12 ([(0,5),(1,5),(1,6),(2,4),(2,6),(3,4),(3,5),(3,6)],7) => 12 ([(0,6),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6)],7) => 12 ([(0,6),(1,5),(1,6),(2,4),(2,6),(3,4),(3,5),(3,6)],7) => 12 ([(0,6),(1,5),(1,6),(2,4),(3,4),(3,6),(4,5)],7) => 18 ([(0,6),(1,5),(2,5),(2,6),(3,4),(3,5),(3,6)],7) => 12 ([(0,6),(1,5),(2,5),(2,6),(3,4),(3,5),(4,6)],7) => 34 ([(0,6),(1,5),(2,5),(2,6),(3,4),(4,6)],7) => 34 ([(0,6),(1,5),(2,5),(2,6),(3,4),(4,5),(4,6)],7) => 24 ([(2,6),(3,6),(4,5),(6,4)],7) => 30 ([(2,6),(3,5),(4,5),(5,6)],7) => 90 ([(1,6),(2,5),(3,5),(5,6),(6,4)],7) => 18 ([(0,6),(1,5),(2,5),(5,6),(6,3),(6,4)],7) => 3 ([(1,6),(2,6),(3,4),(6,5)],7) => 30 ([(1,6),(2,6),(4,5),(6,3),(6,4)],7) => 12 ([(1,6),(2,6),(3,5),(6,4),(6,5)],7) => 18 ([(0,6),(1,5),(2,5),(5,3),(5,6),(6,4)],7) => 6 ([(0,6),(1,6),(2,3),(6,4),(6,5)],7) => 8 ([(0,6),(1,6),(5,2),(6,3),(6,4),(6,5)],7) => 6 ([(0,6),(1,6),(2,5),(6,3),(6,4),(6,5)],7) => 6 ([(2,6),(3,6),(4,5),(4,6)],7) => 60 ([(1,6),(2,6),(3,4),(3,6),(6,5)],7) => 24 ([(0,6),(1,6),(2,3),(2,6),(6,4),(6,5)],7) => 6 ([(1,6),(2,6),(3,4),(3,6),(4,5)],7) => 48 ([(1,6),(2,6),(3,4),(3,6),(4,5),(6,5)],7) => 12 ([(0,6),(1,6),(2,3),(2,6),(3,5),(6,4)],7) => 2 ([(0,6),(1,6),(2,4),(2,6),(4,5),(6,3),(6,5)],7) => 2 ([(0,6),(1,6),(2,3),(2,6),(3,4),(3,5)],7) => 14 ([(0,6),(1,6),(2,3),(2,6),(3,4),(3,5),(6,5)],7) => 2 ([(0,6),(1,6),(2,3),(2,6),(3,4),(3,5),(6,4),(6,5)],7) => 2 ([(0,6),(1,6),(2,3),(2,6),(3,5),(5,4)],7) => 20 ([(0,6),(1,6),(2,3),(2,6),(3,5),(5,4),(6,5)],7) => 2 ([(0,6),(1,6),(2,3),(2,6),(3,4),(4,5),(6,5)],7) => 8 ([(1,6),(2,6),(3,4),(3,5)],7) => 24 ([(1,6),(2,6),(3,4),(3,5),(6,3)],7) => 6 ([(1,5),(2,5),(3,4),(3,6),(5,6)],7) => 30 ([(1,4),(2,4),(3,5),(3,6),(4,5),(4,6)],7) => 18 ([(0,5),(0,6),(1,4),(2,4),(4,5),(4,6),(6,3)],7) => 6 ([(0,5),(1,5),(2,4),(2,6),(5,6),(6,3)],7) => 8 ([(0,6),(1,6),(2,3),(2,4),(6,5)],7) => 14 ([(0,6),(1,6),(5,2),(5,3),(6,4),(6,5)],7) => 3 ([(0,6),(1,6),(2,4),(2,5),(6,3),(6,5)],7) => 8 ([(0,6),(1,6),(2,4),(2,5),(6,3),(6,4),(6,5)],7) => 6 ([(1,6),(2,6),(3,4),(3,5),(3,6)],7) => 24 ([(0,6),(1,6),(2,3),(2,4),(2,6),(6,5)],7) => 12 ([(0,6),(1,6),(2,3),(2,4),(2,6),(4,5)],7) => 30 ([(0,6),(1,6),(2,3),(2,4),(2,6),(4,5),(6,5)],7) => 6 ([(0,6),(1,6),(2,3),(2,4),(2,6),(3,5),(4,5)],7) => 16 ([(0,5),(1,5),(2,3),(2,4),(2,5),(3,6),(4,6),(5,6)],7) => 4 ([(0,6),(1,6),(2,3),(2,4),(2,5)],7) => 12 ([(0,6),(1,6),(5,2),(5,3),(5,4),(6,5)],7) => 2 ([(0,5),(1,5),(2,3),(2,4),(2,6),(5,6)],7) => 14 ([(0,4),(1,4),(2,3),(2,5),(2,6),(4,5),(4,6)],7) => 8 ([(0,6),(1,6),(2,3),(2,4),(2,5),(6,3),(6,4),(6,5)],7) => 6 ([(0,6),(1,6),(2,3),(2,4),(2,5),(2,6)],7) => 12 ([(0,6),(1,2),(1,3),(1,5),(4,6),(5,4)],7) => 52 ([(0,3),(0,4),(0,5),(1,6),(2,6),(5,1),(5,2)],7) => 20 ([(0,3),(0,4),(0,5),(1,6),(2,6),(4,2),(5,1)],7) => 5 ([(0,6),(1,6),(2,3),(2,4),(2,5),(5,6)],7) => 76 ([(0,6),(1,2),(1,4),(1,5),(3,6),(4,6),(5,3)],7) => 38 ([(0,3),(0,4),(0,5),(1,6),(2,6),(4,6),(5,1),(5,2)],7) => 15 ([(0,3),(0,4),(0,5),(1,6),(2,6),(3,6),(4,2),(5,1)],7) => 4 ([(0,6),(1,6),(2,3),(2,4),(2,5),(4,6),(5,6)],7) => 52 ([(0,6),(1,3),(1,4),(1,5),(2,6),(3,6),(4,6),(5,2)],7) => 30 ([(0,3),(0,4),(0,5),(1,6),(2,6),(3,6),(4,6),(5,1),(5,2)],7) => 12 ([(0,6),(1,6),(2,3),(2,4),(2,5),(3,6),(4,6),(5,6)],7) => 40 ([(1,6),(2,6),(3,4),(3,5),(5,6)],7) => 108 ([(0,6),(1,6),(2,3),(2,4),(4,6),(6,5)],7) => 24 ([(1,6),(2,6),(3,4),(3,5),(4,6),(5,6)],7) => 72 ([(0,6),(1,6),(2,3),(2,4),(3,6),(4,6),(6,5)],7) => 12 ([(0,6),(1,6),(2,3),(2,4),(4,5)],7) => 30 ([(0,6),(1,6),(4,3),(5,2),(5,4),(6,5)],7) => 2 ([(0,5),(1,5),(2,3),(2,6),(3,4),(5,6)],7) => 2 ([(0,4),(1,4),(2,3),(2,5),(3,6),(4,5),(4,6)],7) => 2 ([(0,4),(1,4),(2,3),(2,5),(3,6),(4,5),(5,6)],7) => 5 ([(0,6),(1,6),(2,4),(2,5),(4,3),(5,3),(6,4),(6,5)],7) => 3 ([(0,5),(1,5),(2,3),(2,4),(4,6),(5,6)],7) => 6 ([(0,6),(1,3),(1,5),(4,6),(5,2),(5,4)],7) => 33 ([(0,4),(0,5),(2,6),(3,6),(5,1),(5,2),(5,3)],7) => 15 ([(0,6),(1,6),(2,3),(2,4),(4,5),(4,6)],7) => 24 ([(0,6),(1,4),(1,5),(3,6),(4,2),(5,3)],7) => 13 ([(0,6),(1,3),(1,4),(2,6),(3,5),(4,2),(6,5)],7) => 11 ([(0,6),(1,4),(1,5),(3,6),(4,3),(5,2),(5,6)],7) => 13 ([(0,4),(0,5),(2,6),(3,6),(4,1),(4,6),(5,2),(5,3)],7) => 5 ([(0,3),(0,4),(1,6),(2,6),(3,5),(3,6),(4,1),(4,2),(4,5)],7) => 5 ([(0,6),(1,3),(1,4),(2,6),(3,5),(3,6),(4,2),(4,5)],7) => 13 ([(0,4),(0,5),(2,6),(3,6),(4,3),(5,1),(5,2)],7) => 3 ([(0,3),(0,4),(1,5),(2,5),(3,2),(3,6),(4,1),(4,6)],7) => 3 ([(0,3),(0,4),(1,6),(2,6),(3,2),(3,5),(4,1),(4,5),(5,6)],7) => 2 ([(0,4),(0,5),(2,6),(3,6),(4,1),(5,2),(5,3)],7) => 5 ([(0,3),(0,4),(1,5),(2,5),(3,6),(4,1),(4,2),(5,6)],7) => 4 ([(0,3),(0,4),(1,5),(2,5),(3,6),(4,1),(4,2),(4,6)],7) => 5 ([(0,3),(0,4),(1,6),(2,6),(3,5),(4,1),(4,2),(4,5),(5,6)],7) => 2 ([(0,6),(1,3),(1,4),(2,6),(3,5),(4,2),(4,5)],7) => 13 ([(0,6),(1,3),(1,4),(2,6),(3,5),(4,2),(4,5),(5,6)],7) => 5 ([(0,3),(0,4),(1,5),(2,5),(3,6),(4,2),(4,6),(6,1)],7) => 2 ([(0,6),(1,6),(2,3),(2,4),(3,5),(4,6)],7) => 12 ([(0,6),(1,6),(2,3),(2,4),(3,6),(4,5),(6,5)],7) => 18 ([(0,6),(1,4),(1,5),(3,6),(4,6),(5,2),(5,3)],7) => 23 ([(0,4),(0,5),(2,6),(3,6),(4,6),(5,1),(5,2),(5,3)],7) => 11 ([(0,6),(1,6),(2,3),(2,4),(3,6),(4,5),(4,6)],7) => 12 ([(0,6),(1,6),(2,3),(2,4),(3,5),(4,6),(5,6)],7) => 40 ([(0,6),(1,4),(1,5),(2,6),(3,6),(4,6),(5,2),(5,3)],7) => 15 ([(0,4),(0,5),(1,6),(2,6),(3,6),(4,6),(5,1),(5,2),(5,3)],7) => 8 ([(0,5),(1,5),(2,3),(2,4),(3,6),(4,6)],7) => 16 ([(0,6),(1,6),(2,5),(3,5),(4,2),(4,3),(6,4)],7) => 1 ([(0,5),(1,5),(2,3),(2,4),(3,6),(4,6),(5,6)],7) => 4 ([(0,6),(1,6),(2,3),(2,4),(3,5),(4,5),(4,6)],7) => 12 ([(0,6),(1,6),(2,3),(2,4),(3,5),(3,6),(4,5),(4,6)],7) => 12 ([(0,5),(1,2),(1,3),(2,6),(3,6),(4,5),(6,4)],7) => 5 ([(0,3),(0,4),(1,5),(2,5),(3,6),(4,6),(6,1),(6,2)],7) => 1 ([(0,6),(1,6),(2,3),(2,4),(3,5),(4,5),(5,6)],7) => 20 ([(0,6),(1,6),(2,3),(2,4),(4,5),(5,6)],7) => 52 ([(0,6),(1,2),(1,5),(3,6),(4,6),(5,3),(5,4)],7) => 19 ([(0,4),(0,5),(1,6),(2,6),(3,6),(5,1),(5,2),(5,3)],7) => 10 ([(0,6),(1,4),(1,5),(2,6),(3,6),(4,3),(5,2)],7) => 5 ([(0,4),(0,5),(1,6),(2,6),(3,6),(4,3),(5,1),(5,2)],7) => 2 ([(2,6),(3,6),(4,5),(5,6)],7) => 180 ([(1,6),(2,6),(3,4),(4,6),(6,5)],7) => 36 ([(0,6),(1,6),(2,3),(3,6),(6,4),(6,5)],7) => 6 ([(1,6),(2,6),(3,4),(4,5)],7) => 48 ([(1,6),(2,6),(3,5),(5,4),(6,3)],7) => 6 ([(1,5),(2,5),(3,4),(4,6),(5,6)],7) => 12 ([(0,5),(1,5),(2,3),(3,6),(5,6),(6,4)],7) => 2 ([(0,6),(1,6),(2,3),(3,5),(6,4)],7) => 2 ([(0,6),(1,6),(4,2),(5,4),(6,3),(6,5)],7) => 3 ([(0,5),(1,5),(2,3),(3,6),(5,4),(5,6)],7) => 2 ([(1,6),(2,6),(3,4),(4,5),(4,6)],7) => 36 ([(0,6),(1,6),(2,3),(3,5),(3,6),(6,4)],7) => 12 ([(0,3),(1,6),(2,6),(3,5),(3,6),(5,4)],7) => 18 ([(0,6),(1,6),(2,3),(3,4),(3,6),(4,5),(6,5)],7) => 6 ([(0,3),(1,6),(2,6),(3,4),(3,5)],7) => 14 ([(0,6),(1,6),(4,5),(5,2),(5,3),(6,4)],7) => 1 ([(0,5),(1,5),(2,3),(3,4),(3,6),(5,6)],7) => 2 ([(0,4),(1,4),(2,3),(3,5),(3,6),(4,5),(4,6)],7) => 2 ([(0,6),(1,5),(4,6),(5,2),(5,3),(5,4)],7) => 24 ([(0,5),(3,6),(4,6),(5,1),(5,2),(5,3),(5,4)],7) => 12 ([(0,3),(1,6),(2,6),(3,4),(3,5),(3,6)],7) => 12 ([(0,3),(1,6),(2,6),(3,4),(3,5),(5,6)],7) => 32 ([(0,6),(1,5),(3,6),(4,6),(5,2),(5,3),(5,4)],7) => 14 ([(0,5),(2,6),(3,6),(4,6),(5,1),(5,2),(5,3),(5,4)],7) => 8 ([(0,3),(1,6),(2,6),(3,4),(3,5),(4,6),(5,6)],7) => 20 ([(0,6),(1,5),(2,6),(3,6),(4,6),(5,2),(5,3),(5,4)],7) => 10 ([(0,5),(1,6),(2,6),(3,6),(4,6),(5,1),(5,2),(5,3),(5,4)],7) => 6 ([(1,3),(2,6),(3,5),(4,6),(5,4)],7) => 24 ([(0,6),(1,5),(2,6),(4,2),(5,4),(6,3)],7) => 4 ([(1,4),(2,6),(3,6),(4,5),(5,2),(5,3)],7) => 6 ([(0,4),(1,6),(2,6),(4,5),(5,1),(5,2),(6,3)],7) => 1 ([(1,6),(2,6),(3,4),(4,5),(5,6)],7) => 72 ([(0,6),(1,6),(2,3),(3,5),(5,6),(6,4)],7) => 12 ([(0,3),(1,6),(2,6),(3,5),(5,4)],7) => 20 ([(0,6),(1,6),(3,4),(4,2),(5,3),(6,5)],7) => 1 ([(0,5),(1,5),(2,3),(3,4),(4,6),(5,6)],7) => 8 ([(0,6),(1,4),(3,6),(4,5),(5,2),(5,3)],7) => 9 ([(0,4),(2,6),(3,6),(4,5),(5,1),(5,2),(5,3)],7) => 3 ([(0,3),(1,6),(2,6),(3,5),(5,4),(5,6)],7) => 12 ([(1,6),(2,6),(3,5),(4,5)],7) => 36 ([(1,6),(2,6),(3,5),(4,5),(4,6)],7) => 36 ([(0,6),(1,6),(2,5),(3,5),(3,6),(5,4)],7) => 18 ([(0,6),(1,6),(2,4),(3,4),(3,6),(4,5),(6,5)],7) => 6 ([(1,6),(2,6),(3,5),(3,6),(4,5),(4,6)],7) => 36 ([(0,6),(1,6),(2,5),(2,6),(3,5),(3,6),(5,4)],7) => 18 ([(0,6),(1,6),(2,4),(2,6),(3,4),(3,6),(4,5),(6,5)],7) => 6 ([(0,6),(1,6),(2,5),(2,6),(3,5),(3,6),(6,4)],7) => 12 ([(1,6),(2,5),(3,5),(3,6),(4,5),(4,6)],7) => 36 ([(0,6),(1,5),(2,5),(2,6),(3,5),(3,6),(6,4)],7) => 14 ([(0,6),(1,5),(2,5),(2,6),(3,5),(3,6),(5,4),(6,4)],7) => 6 ([(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6)],7) => 36 ([(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(5,4)],7) => 14 ([(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(5,4),(6,4)],7) => 6 ([(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(6,4)],7) => 12 ([(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6)],7) => 36 ([(0,5),(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(6,4)],7) => 12 ([(0,5),(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(5,4),(6,4)],7) => 6 ([(0,6),(1,6),(2,5),(3,5),(3,6),(6,4)],7) => 14 ([(1,6),(2,5),(3,5),(4,6),(5,4)],7) => 24 ([(1,5),(2,5),(3,6),(4,6),(5,3),(5,4)],7) => 6 ([(0,6),(1,5),(2,5),(4,6),(5,4),(6,3)],7) => 4 ([(0,6),(1,6),(2,5),(3,5),(5,4),(6,2),(6,3)],7) => 1 ([(1,6),(2,6),(3,5),(4,5),(5,6)],7) => 72 ([(0,6),(1,6),(2,5),(3,5),(5,6),(6,4)],7) => 12 ([(0,6),(1,6),(2,5),(3,5),(6,4)],7) => 18 ([(0,6),(1,5),(2,5),(4,6),(5,3),(5,4)],7) => 9 ([(0,6),(1,6),(3,5),(4,5),(6,2),(6,3),(6,4)],7) => 3 ([(0,6),(1,6),(2,5),(3,5),(5,4),(5,6)],7) => 12 ([(0,5),(1,5),(2,4),(3,4),(4,6),(5,6)],7) => 6 ([(0,6),(1,6),(2,5),(3,4)],7) => 12 ([(0,6),(1,6),(2,3),(4,5),(6,4)],7) => 9 ([(0,6),(1,6),(4,3),(5,2),(6,4),(6,5)],7) => 1 ([(0,6),(1,6),(2,5),(3,4),(6,3),(6,5)],7) => 7 ([(0,6),(1,5),(2,5),(3,4),(5,6)],7) => 22 ([(0,4),(1,4),(2,6),(3,5),(4,5),(4,6)],7) => 12 ([(0,6),(1,5),(2,5),(3,4),(5,6),(6,3)],7) => 3 ([(0,4),(1,4),(2,5),(3,6),(4,6),(6,5)],7) => 15 ([(0,6),(1,6),(2,5),(3,4),(3,6)],7) => 12 ([(0,6),(1,6),(2,3),(2,6),(4,5),(6,4)],7) => 6 ([(0,6),(1,6),(2,5),(3,4),(3,6),(6,5)],7) => 18 ([(0,6),(1,6),(2,5),(3,4),(3,6),(4,5)],7) => 34 ([(0,6),(1,6),(2,3),(2,6),(3,5),(4,5),(6,4)],7) => 4 ([(0,6),(1,5),(2,5),(3,4),(3,5),(4,6),(5,6)],7) => 10 ([(0,6),(1,6),(2,5),(2,6),(3,4),(3,6)],7) => 12 ([(0,6),(1,6),(2,5),(2,6),(3,4),(3,6),(4,5)],7) => 30 ([(0,6),(1,6),(2,5),(2,6),(3,4),(3,5)],7) => 12 ([(0,6),(1,6),(2,4),(2,6),(3,4),(3,5),(6,5)],7) => 14 ([(0,6),(1,6),(2,5),(2,6),(3,4),(3,5),(3,6)],7) => 12 ([(0,6),(1,6),(2,5),(2,6),(3,4),(3,5),(4,6)],7) => 44 ([(0,6),(1,6),(2,5),(3,4),(3,6),(5,6)],7) => 44 ([(0,6),(1,6),(2,5),(2,6),(3,4),(4,5)],7) => 30 ([(0,6),(1,6),(2,5),(2,6),(3,4),(4,5),(4,6)],7) => 24 ([(0,5),(1,5),(2,6),(3,4),(3,6)],7) => 12 ([(0,5),(1,4),(2,4),(2,6),(3,5),(3,6)],7) => 12 ([(0,6),(1,4),(2,5),(2,6),(3,4),(3,5),(3,6)],7) => 12 ([(0,6),(1,5),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6)],7) => 12 ([(0,5),(1,4),(1,5),(2,4),(2,6),(3,6),(5,3)],7) => 9 ([(0,6),(1,5),(2,4),(2,6),(3,4),(3,5),(5,6)],7) => 22 ([(0,6),(1,5),(2,5),(3,4),(3,6),(5,3)],7) => 4 ([(0,4),(1,5),(2,5),(3,4),(3,6),(5,6)],7) => 18 ([(0,6),(1,5),(1,6),(2,4),(3,4),(4,5),(4,6)],7) => 12 ([(0,5),(1,5),(2,3),(2,6),(4,6),(5,4)],7) => 9 ([(0,6),(1,6),(3,5),(4,2),(4,5),(6,3),(6,4)],7) => 1 ([(0,5),(1,5),(2,4),(2,6),(3,6),(5,3),(5,4)],7) => 7 ([(0,6),(1,5),(2,5),(3,4),(3,6),(5,6)],7) => 22 ([(0,6),(1,6),(2,5),(3,4),(3,5),(3,6)],7) => 12 ([(0,6),(1,6),(2,5),(3,4),(3,5),(4,6)],7) => 44 ([(0,6),(1,5),(2,3),(2,5),(3,6),(4,6),(5,4)],7) => 10 ([(0,5),(1,2),(1,5),(2,6),(3,6),(4,6),(5,3),(5,4)],7) => 3 ([(0,6),(1,6),(2,5),(3,4),(3,5),(4,6),(5,6)],7) => 20 ([(0,4),(1,4),(2,5),(2,6),(3,5),(3,6)],7) => 12 ([(0,5),(1,4),(1,6),(2,4),(2,6),(3,5),(3,6)],7) => 12 ([(0,5),(0,6),(1,5),(1,6),(2,4),(3,4),(3,5),(3,6)],7) => 12 ([(0,6),(1,4),(1,5),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6)],7) => 12 ([(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6)],7) => 12 ([(0,5),(0,6),(1,5),(1,6),(2,4),(3,4),(3,5),(4,6)],7) => 18 ([(0,5),(0,6),(1,5),(1,6),(2,4),(2,6),(3,4),(3,6)],7) => 12 ([(0,5),(0,6),(1,5),(1,6),(2,4),(2,6),(3,4),(3,6),(4,5)],7) => 18 ([(0,5),(0,6),(1,5),(1,6),(2,4),(2,6),(3,4),(3,5)],7) => 12 ([(0,5),(0,6),(1,5),(1,6),(2,4),(2,6),(3,4),(3,5),(3,6)],7) => 12 ([(0,5),(0,6),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6)],7) => 12 ([(0,5),(0,6),(1,4),(1,6),(2,4),(2,5),(3,4),(3,5),(3,6)],7) => 12 ([(0,5),(0,6),(1,4),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6)],7) => 12 ([(0,5),(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6)],7) => 12 ([(0,4),(0,5),(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6)],7) => 12 ([(0,6),(1,5),(1,6),(2,4),(2,5),(3,4),(3,5),(4,6)],7) => 22 ([(0,5),(0,6),(1,4),(1,6),(2,4),(2,6),(3,5),(4,3)],7) => 9 ([(0,4),(1,4),(2,5),(2,6),(3,5),(3,6),(4,3)],7) => 4 ([(0,6),(1,6),(2,4),(2,5),(3,4),(3,5),(6,2),(6,3)],7) => 1 ([(0,5),(1,5),(2,4),(2,6),(3,4),(3,6),(5,6)],7) => 18 ([(0,5),(0,6),(1,5),(1,6),(2,4),(3,4),(4,5),(4,6)],7) => 12 ([(0,6),(1,6),(2,4),(2,5),(3,4),(3,5),(3,6)],7) => 12 ([(0,6),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6)],7) => 12 ([(0,6),(1,4),(1,5),(2,4),(2,5),(3,6),(5,3)],7) => 14 ([(0,5),(0,6),(1,5),(1,6),(2,4),(3,4),(6,2),(6,3)],7) => 4 ([(0,3),(1,5),(1,6),(2,5),(2,6),(4,3),(5,4),(6,4)],7) => 5 ([(0,5),(0,6),(1,5),(1,6),(2,4),(3,4),(5,3),(6,2)],7) => 1 ([(0,5),(0,6),(1,5),(1,6),(2,3),(4,3),(5,4),(6,2),(6,4)],7) => 1 ([(0,5),(0,6),(1,5),(1,6),(3,2),(4,2),(5,3),(5,4),(6,3),(6,4)],7) => 1 ([(0,6),(1,6),(2,4),(2,5),(3,4),(3,5),(5,6)],7) => 32 ([(0,6),(1,4),(1,5),(2,4),(2,5),(3,6),(4,6),(5,3)],7) => 10 ([(0,4),(0,5),(1,4),(1,5),(2,6),(3,6),(4,6),(5,2),(5,3)],7) => 3 ([(0,6),(1,6),(2,4),(2,5),(3,4),(3,5),(4,6),(5,6)],7) => 20 ([(0,6),(1,5),(2,3),(2,5),(4,6),(5,4)],7) => 14 ([(0,6),(1,2),(1,6),(3,5),(4,5),(6,3),(6,4)],7) => 4 ([(0,6),(1,6),(2,5),(3,4),(3,5),(5,6)],7) => 32 ([(0,6),(1,6),(2,4),(3,5),(5,6)],7) => 44 ([(0,6),(1,6),(2,3),(3,6),(4,5),(6,4)],7) => 6 ([(0,6),(1,6),(2,5),(3,4),(4,6),(6,5)],7) => 30 ([(0,6),(1,6),(2,5),(3,4),(4,6),(5,6)],7) => 20 ([(0,6),(1,5),(2,5),(3,4),(4,6)],7) => 34 ([(0,6),(1,6),(2,5),(3,4),(4,5),(6,3)],7) => 5 ([(0,5),(1,5),(2,3),(3,6),(4,6),(5,4)],7) => 5 ([(0,6),(1,6),(2,5),(3,5),(4,3),(6,2),(6,4)],7) => 2 ([(0,5),(1,5),(2,4),(3,6),(4,6),(5,3),(5,4)],7) => 3 ([(0,6),(1,5),(2,5),(3,4),(4,6),(5,6)],7) => 10 ([(0,6),(1,6),(2,5),(3,4),(4,5),(4,6)],7) => 24 ([(0,6),(1,5),(2,3),(3,6),(4,5),(6,4)],7) => 10 ([(0,6),(1,2),(2,6),(3,5),(4,5),(6,3),(6,4)],7) => 2 ([(0,6),(1,6),(2,5),(3,4),(4,5),(5,6)],7) => 40 ([(3,6),(4,5)],7) => 120 ([(3,6),(4,5),(4,6)],7) => 120 ([(2,6),(3,4),(3,6),(4,5)],7) => 90 ([(1,6),(2,3),(2,6),(3,4),(3,5)],7) => 30 ([(0,6),(1,5),(1,6),(5,2),(5,3),(5,4)],7) => 14 ([(0,6),(1,4),(1,6),(4,2),(4,3),(4,5),(6,5)],7) => 2 ([(0,6),(1,3),(1,6),(3,2),(3,4),(3,5),(6,4),(6,5)],7) => 2 ([(0,6),(1,2),(1,6),(2,3),(2,4),(2,5),(6,3),(6,4),(6,5)],7) => 2 ([(1,5),(2,3),(2,5),(3,4),(3,6),(5,6)],7) => 6 ([(1,4),(2,3),(2,4),(3,5),(3,6),(4,5),(4,6)],7) => 6 ([(0,5),(1,4),(1,5),(4,3),(4,6),(5,6),(6,2)],7) => 2 ([(0,6),(1,5),(1,6),(5,2),(5,3),(6,4)],7) => 2 ([(0,6),(1,4),(1,6),(4,3),(4,5),(6,2),(6,5)],7) => 2 ([(0,6),(1,3),(1,6),(3,4),(3,5),(6,2),(6,4),(6,5)],7) => 2 ([(2,5),(3,4),(3,5),(4,6),(5,6)],7) => 30 ([(1,5),(2,3),(2,5),(3,6),(5,6),(6,4)],7) => 6 ([(0,5),(1,4),(1,5),(4,6),(5,6),(6,2),(6,3)],7) => 1 ([(1,6),(2,3),(2,6),(3,5),(6,4)],7) => 6 ([(1,5),(2,3),(2,5),(3,6),(5,4),(5,6)],7) => 6 ([(0,6),(1,5),(1,6),(5,2),(6,3),(6,4)],7) => 2 ([(0,6),(1,4),(1,6),(4,5),(6,2),(6,3),(6,5)],7) => 2 ([(1,6),(2,3),(2,6),(3,5),(5,4)],7) => 36 ([(1,5),(2,3),(2,5),(3,4),(4,6),(5,6)],7) => 18 ([(0,5),(1,4),(1,5),(3,6),(4,3),(5,6),(6,2)],7) => 3 ([(0,6),(1,5),(1,6),(4,2),(5,4),(6,3)],7) => 4 ([(0,6),(1,3),(1,6),(3,5),(5,4),(6,2),(6,5)],7) => 2 ([(0,6),(1,4),(1,6),(3,5),(4,3),(6,2),(6,5)],7) => 4 ([(0,6),(1,4),(1,6),(4,5),(5,2),(5,3)],7) => 9 ([(0,6),(1,3),(1,6),(3,4),(4,2),(4,5),(6,5)],7) => 3 ([(0,6),(1,2),(1,6),(2,3),(3,4),(3,5),(6,4),(6,5)],7) => 3 ([(3,5),(3,6),(4,5),(4,6)],7) => 120 ([(2,5),(2,6),(3,5),(3,6),(6,4)],7) => 60 ([(1,5),(1,6),(2,5),(2,6),(6,3),(6,4)],7) => 18 ([(0,5),(0,6),(1,5),(1,6),(6,2),(6,3),(6,4)],7) => 8 ([(2,4),(2,5),(3,4),(3,5),(4,6),(5,6)],7) => 30 ([(1,4),(1,5),(2,4),(2,5),(4,6),(5,6),(6,3)],7) => 6 ([(1,5),(1,6),(2,5),(2,6),(5,4),(6,3)],7) => 6 ([(1,4),(1,6),(2,4),(2,6),(4,5),(6,3),(6,5)],7) => 6 ([(1,5),(1,6),(2,5),(2,6),(5,3),(5,4),(6,3),(6,4)],7) => 6 ([(0,5),(0,6),(1,5),(1,6),(5,4),(6,2),(6,3)],7) => 2 ([(0,5),(0,6),(1,5),(1,6),(5,4),(6,2),(6,3),(6,4)],7) => 2 ([(0,5),(0,6),(1,5),(1,6),(5,3),(5,4),(6,2),(6,4)],7) => 2 ([(0,5),(0,6),(1,5),(1,6),(5,3),(5,4),(6,2),(6,3),(6,4)],7) => 2 ([(0,5),(0,6),(1,5),(1,6),(5,2),(5,3),(5,4),(6,2),(6,3),(6,4)],7) => 2 ([(1,5),(1,6),(2,5),(2,6),(3,4)],7) => 24 ([(1,6),(2,4),(2,5),(3,4),(3,5),(3,6)],7) => 24 ([(0,4),(1,5),(1,6),(2,4),(2,5),(2,6),(6,3)],7) => 16 ([(0,4),(1,5),(1,6),(2,4),(2,5),(2,6),(5,3),(6,3)],7) => 8 ([(0,6),(1,4),(1,5),(2,4),(2,5),(2,6),(5,3),(6,3)],7) => 6 ([(0,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,6),(4,6),(5,6)],7) => 4 ([(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6)],7) => 24 ([(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(5,3)],7) => 16 ([(0,6),(1,3),(1,4),(1,6),(2,3),(2,4),(2,6),(3,5),(4,5)],7) => 8 ([(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,6),(4,6),(5,6)],7) => 4 ([(0,6),(1,3),(1,4),(1,6),(2,3),(2,4),(2,6),(4,5),(6,5)],7) => 6 ([(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(6,3)],7) => 12 ([(0,6),(1,4),(1,5),(2,4),(2,5),(2,6),(6,3)],7) => 14 ([(1,5),(1,6),(2,5),(2,6),(3,4),(6,3)],7) => 18 ([(0,5),(0,6),(1,5),(1,6),(4,3),(5,4),(6,2)],7) => 3 ([(0,5),(0,6),(1,5),(1,6),(2,3),(5,4),(6,2),(6,4)],7) => 3 ([(0,5),(0,6),(1,5),(1,6),(4,2),(5,3),(5,4),(6,3),(6,4)],7) => 2 ([(0,5),(0,6),(1,5),(1,6),(2,4),(5,2),(5,3),(6,3),(6,4)],7) => 3 ([(0,5),(0,6),(1,5),(1,6),(4,3),(5,4),(6,2),(6,4)],7) => 2 ([(0,5),(0,6),(1,5),(1,6),(3,4),(5,3),(6,2),(6,4)],7) => 3 ([(1,6),(2,4),(2,5),(3,4),(3,5),(5,6)],7) => 42 ([(1,4),(1,5),(2,4),(2,5),(3,6),(4,6),(5,3)],7) => 12 ([(1,6),(2,4),(2,5),(3,4),(3,5),(4,6),(5,6)],7) => 24 ([(0,6),(1,4),(1,5),(2,4),(2,5),(4,6),(5,6),(6,3)],7) => 4 ([(0,5),(1,4),(1,6),(2,4),(2,6),(4,5),(6,3)],7) => 4 ([(0,6),(1,4),(1,5),(2,4),(2,5),(4,6),(5,3),(5,6)],7) => 4 ([(0,6),(1,4),(1,5),(2,4),(2,5),(5,6),(6,3)],7) => 10 ([(0,4),(1,5),(1,6),(2,5),(2,6),(4,3),(5,4),(6,3)],7) => 7 ([(0,5),(0,6),(1,5),(1,6),(2,4),(6,3)],7) => 16 ([(0,5),(0,6),(1,5),(1,6),(4,3),(6,2),(6,4)],7) => 8 ([(0,5),(0,6),(1,5),(1,6),(3,4),(5,2),(5,3),(6,4)],7) => 5 ([(0,5),(1,4),(1,6),(2,4),(2,6),(6,3),(6,5)],7) => 10 ([(0,4),(0,5),(1,4),(1,5),(2,3),(4,6),(5,6)],7) => 8 ([(0,4),(1,5),(1,6),(2,5),(2,6),(5,3),(6,3),(6,4)],7) => 4 ([(0,6),(1,3),(1,4),(2,3),(2,4),(3,5),(3,6),(4,5),(4,6)],7) => 4 ([(1,5),(1,6),(2,5),(2,6),(3,4),(3,6)],7) => 24 ([(0,5),(0,6),(1,5),(1,6),(2,3),(2,6),(6,4)],7) => 12 ([(1,5),(1,6),(2,4),(2,6),(3,4),(3,6),(4,5)],7) => 30 ([(0,5),(0,6),(1,4),(1,6),(2,4),(2,6),(4,5),(6,3)],7) => 2 ([(0,5),(0,6),(1,4),(1,6),(2,4),(2,6),(4,5),(5,3)],7) => 8 ([(0,3),(0,6),(1,3),(1,6),(2,5),(2,6),(3,5),(5,4),(6,4)],7) => 5 ([(0,5),(0,6),(1,5),(1,6),(2,3),(2,6),(5,4)],7) => 14 ([(0,4),(0,6),(1,4),(1,6),(2,3),(2,6),(4,5),(6,5)],7) => 6 ([(0,5),(0,6),(1,5),(1,6),(2,4),(2,6),(5,3),(5,4)],7) => 8 ([(0,3),(0,6),(1,3),(1,6),(2,4),(2,6),(3,4),(3,5),(6,5)],7) => 2 ([(1,5),(1,6),(2,5),(2,6),(3,4),(3,5),(3,6)],7) => 24 ([(0,5),(0,6),(1,5),(1,6),(2,4),(2,5),(2,6),(6,3)],7) => 12 ([(0,5),(0,6),(1,5),(1,6),(2,3),(2,5),(2,6),(5,4),(6,4)],7) => 6 ([(0,5),(0,6),(1,5),(1,6),(2,3),(2,5),(2,6),(3,4)],7) => 20 ([(0,5),(0,6),(1,5),(1,6),(2,3),(2,5),(2,6),(3,4),(6,4)],7) => 6 ([(0,4),(0,5),(1,4),(1,5),(2,3),(2,4),(2,5),(3,6),(4,6),(5,6)],7) => 4 ([(1,5),(1,6),(2,5),(2,6),(3,4),(3,5),(4,6)],7) => 48 ([(0,5),(0,6),(1,5),(1,6),(2,3),(2,5),(3,6),(5,4)],7) => 2 ([(0,5),(0,6),(1,5),(1,6),(2,3),(2,5),(3,6),(5,4),(6,4)],7) => 8 ([(0,5),(0,6),(1,5),(1,6),(2,3),(2,5),(3,6),(6,4)],7) => 14 ([(0,5),(0,6),(1,5),(1,6),(2,3),(2,6),(3,4)],7) => 20 ([(0,4),(0,6),(1,4),(1,6),(2,3),(2,6),(3,5),(6,5)],7) => 6 ([(0,4),(0,6),(1,4),(1,6),(2,3),(2,6),(3,5),(4,5)],7) => 6 ([(0,4),(0,5),(1,4),(1,5),(2,3),(2,5),(3,6),(4,6),(5,6)],7) => 4 ([(0,5),(0,6),(1,5),(1,6),(2,3),(2,5),(3,4),(3,6)],7) => 14 ([(0,5),(0,6),(1,5),(1,6),(2,3),(2,5),(3,4),(3,6),(5,4)],7) => 2 ([(0,5),(0,6),(1,5),(1,6),(2,3),(2,5),(3,4),(4,6)],7) => 20 ([(0,5),(0,6),(1,5),(1,6),(2,3),(2,4)],7) => 12 ([(0,5),(0,6),(1,5),(1,6),(4,2),(4,3),(6,4)],7) => 4 ([(0,5),(0,6),(1,5),(1,6),(4,2),(4,3),(5,4),(6,4)],7) => 1 ([(0,5),(0,6),(1,5),(1,6),(3,2),(3,4),(5,3),(6,4)],7) => 2 ([(0,5),(0,6),(1,5),(1,6),(2,3),(2,4),(5,2),(6,3),(6,4)],7) => 2 ([(0,4),(0,5),(1,4),(1,5),(2,3),(2,6),(5,6)],7) => 16 ([(0,3),(0,4),(1,5),(1,6),(2,5),(2,6),(6,3),(6,4)],7) => 10 ([(0,4),(0,5),(1,4),(1,5),(2,3),(2,6),(4,6),(5,6)],7) => 8 ([(0,3),(0,4),(1,5),(1,6),(2,5),(2,6),(5,4),(6,3)],7) => 4 ([(0,5),(0,6),(1,3),(1,4),(2,3),(2,4),(3,6),(4,5),(4,6)],7) => 4 ([(0,5),(0,6),(1,3),(1,4),(2,3),(2,4),(3,5),(3,6),(4,5),(4,6)],7) => 4 ([(0,5),(0,6),(1,5),(1,6),(2,3),(2,4),(2,6)],7) => 12 ([(0,4),(0,6),(1,4),(1,6),(2,3),(2,5),(2,6),(4,5)],7) => 14 ([(0,3),(0,6),(1,3),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5)],7) => 8 ([(0,5),(0,6),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6)],7) => 12 ([(0,5),(0,6),(1,5),(1,6),(2,3),(2,4),(2,5),(4,6)],7) => 30 ([(0,5),(0,6),(1,5),(1,6),(2,3),(2,4),(2,5),(3,6),(4,6)],7) => 16 ([(0,5),(0,6),(1,2),(1,4),(3,5),(3,6),(4,3)],7) => 14 ([(0,3),(0,4),(1,5),(1,6),(2,5),(2,6),(4,1),(4,2)],7) => 5 ([(0,3),(0,4),(1,5),(1,6),(2,5),(2,6),(3,2),(4,1)],7) => 1 ([(0,5),(0,6),(1,5),(1,6),(2,3),(2,4),(4,6)],7) => 30 ([(0,4),(0,6),(1,4),(1,6),(2,3),(2,5),(3,6),(4,5)],7) => 2 ([(0,5),(0,6),(1,5),(1,6),(2,3),(2,4),(4,5),(4,6)],7) => 24 ([(0,5),(0,6),(1,3),(1,4),(2,5),(2,6),(3,5),(3,6),(4,2)],7) => 8 ([(0,3),(0,4),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,1),(4,2)],7) => 3 ([(0,5),(0,6),(1,2),(1,4),(2,6),(3,5),(3,6),(4,3)],7) => 8 ([(0,3),(0,4),(1,5),(1,6),(2,5),(2,6),(3,6),(4,1),(4,2)],7) => 3 ([(0,5),(0,6),(1,5),(1,6),(2,3),(2,4),(3,6),(4,6)],7) => 16 ([(0,5),(0,6),(1,5),(1,6),(2,3),(2,4),(3,6),(4,5)],7) => 12 ([(0,5),(0,6),(1,5),(1,6),(2,3),(2,4),(3,6),(4,5),(4,6)],7) => 12 ([(0,5),(0,6),(1,5),(1,6),(2,3),(2,4),(3,5),(3,6),(4,5),(4,6)],7) => 12 ([(1,5),(1,6),(2,5),(2,6),(3,4),(4,6)],7) => 48 ([(0,5),(0,6),(1,5),(1,6),(2,3),(3,6),(6,4)],7) => 14 ([(0,5),(0,6),(1,5),(1,6),(2,3),(3,6),(5,4)],7) => 2 ([(0,4),(0,6),(1,4),(1,6),(2,3),(3,6),(4,5),(6,5)],7) => 8 ([(1,5),(1,6),(2,5),(2,6),(3,4),(4,5),(4,6)],7) => 36 ([(0,5),(0,6),(1,5),(1,6),(2,4),(4,5),(4,6),(6,3)],7) => 12 ([(0,5),(0,6),(1,5),(1,6),(2,3),(3,5),(3,6),(5,4),(6,4)],7) => 6 ([(0,5),(0,6),(1,5),(1,6),(2,3),(3,4)],7) => 20 ([(0,5),(0,6),(1,5),(1,6),(3,4),(4,2),(6,3)],7) => 4 ([(0,5),(0,6),(1,5),(1,6),(2,3),(4,2),(5,4),(6,4)],7) => 1 ([(0,5),(0,6),(1,5),(1,6),(3,4),(4,2),(5,3),(6,4)],7) => 2 ([(0,5),(0,6),(1,5),(1,6),(2,3),(3,4),(5,2),(6,4)],7) => 3 ([(0,4),(0,5),(1,4),(1,5),(2,3),(3,6),(5,6)],7) => 6 ([(0,4),(0,5),(1,4),(1,5),(2,3),(3,6),(4,6),(5,6)],7) => 4 ([(0,5),(0,6),(1,4),(3,5),(3,6),(4,2),(4,3)],7) => 10 ([(0,4),(2,5),(2,6),(3,5),(3,6),(4,1),(4,2),(4,3)],7) => 4 ([(0,5),(0,6),(1,5),(1,6),(2,3),(3,4),(3,6)],7) => 14 ([(0,4),(0,6),(1,4),(1,6),(2,3),(3,5),(3,6),(4,5)],7) => 2 ([(0,5),(0,6),(1,5),(1,6),(2,3),(3,4),(3,5),(3,6)],7) => 12 ([(0,5),(0,6),(1,5),(1,6),(2,3),(3,4),(3,6),(4,5)],7) => 18 ([(0,5),(0,6),(1,5),(1,6),(2,3),(3,4),(4,6)],7) => 20 ([(0,5),(0,6),(1,4),(2,6),(3,5),(3,6),(4,2),(4,3)],7) => 4 ([(0,4),(1,6),(2,5),(2,6),(3,5),(3,6),(4,1),(4,2),(4,3)],7) => 2 ([(0,5),(0,6),(1,5),(1,6),(2,3),(3,4),(4,5),(4,6)],7) => 12 ([(0,5),(0,6),(1,4),(2,5),(2,6),(3,5),(3,6),(4,2),(4,3)],7) => 4 ([(0,4),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,1),(4,2),(4,3)],7) => 2 ([(2,6),(3,4),(3,6),(6,5)],7) => 60 ([(1,6),(2,3),(2,6),(6,4),(6,5)],7) => 18 ([(0,6),(1,2),(1,6),(6,3),(6,4),(6,5)],7) => 8 ([(2,6),(3,4),(3,5)],7) => 60 ([(2,6),(3,4),(3,5),(3,6)],7) => 60 ([(1,6),(2,3),(2,4),(2,6),(4,5)],7) => 60 ([(0,6),(1,4),(1,5),(1,6),(5,2),(5,3)],7) => 22 ([(0,6),(1,3),(1,4),(1,6),(4,2),(4,5),(6,5)],7) => 4 ([(0,6),(1,2),(1,3),(1,6),(3,4),(3,5),(6,4),(6,5)],7) => 4 ([(1,5),(2,3),(2,4),(2,5),(4,6),(5,6)],7) => 18 ([(0,5),(1,3),(1,4),(1,5),(4,6),(5,6),(6,2)],7) => 4 ([(0,6),(1,3),(1,5),(1,6),(5,2),(6,4)],7) => 4 ([(0,6),(1,3),(1,4),(1,6),(4,5),(6,2),(6,5)],7) => 4 ([(1,5),(2,3),(2,4),(2,5),(3,6),(4,6)],7) => 30 ([(1,5),(2,3),(2,4),(2,5),(3,6),(4,6),(5,6)],7) => 12 ([(0,5),(1,2),(1,3),(1,5),(2,6),(3,6),(5,6),(6,4)],7) => 2 ([(0,6),(1,3),(1,4),(1,6),(3,5),(4,5),(6,2)],7) => 2 ([(0,5),(1,2),(1,3),(1,5),(2,6),(3,6),(5,4),(5,6)],7) => 2 ([(0,5),(1,3),(1,4),(1,5),(3,6),(4,6),(6,2)],7) => 9 ([(0,6),(1,2),(1,3),(1,6),(2,5),(3,5),(5,4),(6,4)],7) => 5 ([(0,6),(1,4),(1,5),(1,6),(4,3),(5,2)],7) => 8 ([(0,6),(1,3),(1,4),(1,6),(3,5),(4,2),(4,5)],7) => 8 ([(0,6),(1,2),(1,3),(1,6),(2,5),(3,4),(3,5),(6,4)],7) => 2 ([(0,4),(1,2),(1,3),(1,4),(2,6),(3,5),(3,6),(4,5),(4,6)],7) => 2 ([(0,5),(1,3),(1,4),(1,5),(3,6),(4,2),(4,6),(5,6)],7) => 2 ([(0,6),(1,2),(1,3),(1,6),(2,4),(2,5),(3,4),(3,5)],7) => 8 ([(0,4),(1,2),(1,3),(1,4),(2,5),(2,6),(3,5),(3,6),(4,6)],7) => 2 ([(0,4),(1,2),(1,3),(1,4),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6)],7) => 2 ([(0,6),(1,3),(1,4),(1,6),(3,5),(4,2),(6,5)],7) => 2 ([(0,6),(1,2),(1,3),(1,6),(2,5),(3,4),(6,4),(6,5)],7) => 2 ([(1,6),(2,3),(2,4),(2,6),(6,5)],7) => 36 ([(0,6),(1,2),(1,3),(1,6),(6,4),(6,5)],7) => 12 ([(1,6),(2,3),(2,4),(2,5)],7) => 36 ([(1,6),(2,3),(2,4),(2,5),(2,6)],7) => 36 ([(0,6),(1,3),(1,4),(1,5),(1,6),(5,2)],7) => 44 ([(0,6),(1,2),(1,3),(1,4),(1,6),(4,5),(6,5)],7) => 12 ([(0,6),(1,2),(1,3),(1,4),(1,6),(3,5),(4,5)],7) => 22 ([(0,5),(1,2),(1,3),(1,4),(1,5),(3,6),(4,6),(5,6)],7) => 8 ([(0,5),(1,2),(1,3),(1,4),(1,5),(2,6),(3,6),(4,6)],7) => 14 ([(0,5),(1,2),(1,3),(1,4),(1,5),(2,6),(3,6),(4,6),(5,6)],7) => 6 ([(0,6),(1,2),(1,3),(1,4),(1,6),(6,5)],7) => 24 ([(0,6),(1,2),(1,3),(1,4),(1,5)],7) => 24 ([(0,6),(1,2),(1,3),(1,4),(1,5),(1,6)],7) => 24 ([(0,2),(0,3),(0,4),(0,6),(5,1),(6,5)],7) => 60 ([(0,6),(1,2),(1,3),(1,4),(1,5),(5,6)],7) => 84 ([(0,2),(0,3),(0,4),(0,5),(1,6),(4,6),(5,1)],7) => 40 ([(0,6),(1,2),(1,3),(1,4),(1,5),(4,6),(5,6)],7) => 52 ([(0,2),(0,3),(0,4),(0,5),(1,6),(3,6),(4,6),(5,1)],7) => 30 ([(0,6),(1,2),(1,3),(1,4),(1,5),(3,6),(4,6),(5,6)],7) => 38 ([(0,2),(0,3),(0,4),(0,5),(1,6),(2,6),(3,6),(4,6),(5,1)],7) => 24 ([(0,6),(1,2),(1,3),(1,4),(1,5),(2,6),(3,6),(4,6),(5,6)],7) => 30 ([(0,5),(1,2),(1,3),(1,4),(1,6),(5,6)],7) => 30 ([(0,4),(1,2),(1,3),(1,5),(1,6),(4,5),(4,6)],7) => 18 ([(0,3),(1,2),(1,4),(1,5),(1,6),(3,4),(3,5),(3,6)],7) => 14 ([(0,2),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6)],7) => 12 ([(1,3),(1,4),(1,6),(5,2),(6,5)],7) => 72 ([(0,3),(0,4),(0,5),(5,6),(6,1),(6,2)],7) => 20 ([(1,6),(2,3),(2,4),(2,5),(5,6)],7) => 108 ([(0,6),(1,2),(1,3),(1,4),(4,6),(6,5)],7) => 32 ([(1,2),(1,4),(1,5),(3,6),(4,6),(5,3)],7) => 48 ([(0,3),(0,4),(0,5),(1,6),(4,6),(5,1),(6,2)],7) => 10 ([(1,6),(2,3),(2,4),(2,5),(4,6),(5,6)],7) => 66 ([(0,6),(1,2),(1,3),(1,4),(3,6),(4,6),(6,5)],7) => 14 ([(1,3),(1,4),(1,5),(2,6),(3,6),(4,6),(5,2)],7) => 36 ([(0,3),(0,4),(0,5),(1,6),(3,6),(4,6),(5,1),(6,2)],7) => 6 ([(1,6),(2,3),(2,4),(2,5),(3,6),(4,6),(5,6)],7) => 48 ([(0,6),(1,2),(1,3),(1,4),(2,6),(3,6),(4,6),(6,5)],7) => 8 ([(0,6),(1,3),(1,4),(1,5),(3,6),(4,6),(5,2)],7) => 8 ([(0,6),(1,2),(1,3),(1,4),(2,6),(3,6),(4,5),(6,5)],7) => 11 ([(0,3),(0,4),(0,5),(2,6),(3,6),(4,6),(5,1),(5,2)],7) => 18 ([(0,6),(1,3),(1,4),(1,5),(3,6),(4,6),(5,2),(5,6)],7) => 8 ([(0,6),(1,3),(1,4),(1,5),(4,6),(5,2)],7) => 14 ([(0,6),(1,2),(1,3),(1,4),(3,6),(4,5),(6,5)],7) => 23 ([(0,3),(0,4),(0,5),(2,6),(4,6),(5,1),(5,2)],7) => 25 ([(0,6),(1,3),(1,4),(1,5),(4,6),(5,2),(5,6)],7) => 14 ----------------------------------------------------------------------------- Created: May 03, 2020 at 17:31 by Martin Rubey ----------------------------------------------------------------------------- Last Updated: May 03, 2020 at 17:47 by Martin Rubey